Cộng số đo góc, góc kề nhau, góc phụ nhau, góc bù nhau

1. Tính chất cộng số đo hai góc

Nếu tia $Oy$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;">

nằm giữa hai tia $Ox$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;">

và $Oz$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;">

thì

$\displaystyle \widehat{xOy}+\widehat{yOz}=\widehat{xOz}$
Cộng số đo góc, góc kề nhau, góc phụ nhau, góc bù nhau
Ngược lại, nếu $\displaystyle \widehat{xOy}+\widehat{yOz}=\widehat{xOz}$ thì tia $Oy$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;">

nằm giữa hai tia $Ox$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;">

và $Oz$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;">

.

*Lưu ý:

a) Ta có thể dùng mệnh đề tương đương sau với tính chất trên:

Nếu $\displaystyle \widehat{xOy}+\widehat{yOz}\ne \widehat{xOz}$ thì tia $Oy$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;">

không nằm giữa hai tia $Ox$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;">

và $Oz$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;">

.

b) Cộng liên tiếp. Nếu tia $Oy$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;">

nằm giữa hai tia $Ox$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-83d263bdb6449379a43a53d7d5a6846e_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Ox" title="Rendered by QuickLaTeX.com" height="12" width="24" style="vertical-align: 0px;">

và $Ot$ ; tia $Oz$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-897da5de467356e60ee75a184c63d26f_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oz" title="Rendered by QuickLaTeX.com" height="12" width="23" style="vertical-align: 0px;">

nằm giữa hai tia $Oy$

<img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" data-src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="pb-seo-lazy ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;"><noscript><img decoding="async" src="http://abcdonline.vn/wp-content/ql-cache/quicklatex.com-64412b6e9ab1be183bade754dbe140c3_l3.png" class="ql-img-inline-formula quicklatex-auto-format" alt="Oy" title="Rendered by QuickLaTeX.com" height="16" width="23" style="vertical-align: -4px;">

và $Ot$ thì:

$\displaystyle \widehat{xOy}+\widehat{yOz}+\widehat{tOz}=\widehat{xOt}$
Cộng số đo góc, góc kề nhau, góc phụ nhau, góc bù nhau

2. Hai góc kề nhau, phụ nhau, bù nhau

– Hai góc kề nhau là hai góc có một cạnh chung và hai cạnh còn lại nằm trên hai nữa mặt phẳng đối nhau bờ chứa cạnh chung.

– Hai góc phụ nhau là hai góc có tông số đo bằng $90°$

– Hai góc bù nhau là hai góc có tổng số đo bằng $180°$

*Lưu ý:

a) Hai góc kề bù là hai góc vừa kề nhau vừa bù nhau. Hai góc kề bù có tổng số đo bằng $180°$

b) Hai góc cùng phụ (hoặc cùng bù) với một góc thứ $3$ thì bằng nhau.

Hình học 6 - Tags: góc bù nhau, góc kề nhau, góc phụ nhau, số đo góc, toán 6