{"id":2618,"date":"2022-04-22T18:03:00","date_gmt":"2022-04-22T22:03:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=2618"},"modified":"2024-10-25T09:19:35","modified_gmt":"2024-10-25T13:19:35","slug":"geometry-sides-and-angles-of-triangles","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=2618","title":{"rendered":"Geometry &#8211; Sides and Angles of Triangles"},"content":{"rendered":"\n<ol><li>As shown in the diagram below, in $\\triangle{ABC}$, $\\angle{B}\\gt \\angle{C}$, $AD$ is the bisector of the $\\angle{BAC}$, $AE\\perp BC$ at $E$. Prove that $\\angle{DAE}=\\dfrac{1}{2}(\\angle{B}\u2212\\angle{C})$.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" src=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-17-at-5.54.56-PM-1024x632.png\" alt=\"\" class=\"wp-image-2620\" width=\"256\" height=\"158\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-17-at-5.54.56-PM-1024x632.png 1024w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-17-at-5.54.56-PM-300x185.png 300w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-17-at-5.54.56-PM-768x474.png 768w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-17-at-5.54.56-PM.png 1088w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/figure>\n\n\n\n<p>2. There are four points $A$, $B$, $C$, $D$ on the plane, such that any three points are not collinear. Prove that in the triangles $ABC$, $ABD$, $ACD$ and $BCD$ there is at least one triangle which has an interior angle not greater than $45^\\circ$.<\/p>\n\n\n\n<p>3. In $\\triangle{ABC}$, $AB=AC$, $D$, $E$, $F$ are on $AB$, $BC$, $CA$, such that $DE= EF=FD$. Prove that $\\angle{DEB}=\\dfrac{1}{2}(\\angle{ADF}+\\angle{CFE})$.<\/p>\n\n\n\n<p>4. <!-- MOSCOW\/1952 --> In $\\angle{ABC}$, $AC=BC$, $\\angle{C}=20^\\circ$, $M$ is on the side $AC$ and $N$ is on the side $BC$, such that $\\angle{BAN}=50^\\circ$, $\\angle{ABM}=60^\\circ$. Find $\\angle{NMB}$ in degrees.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>As shown in the diagram below, in $\\triangle{ABC}$, $\\angle{B}\\gt \\angle{C}$, $AD$ is the bisector of the $\\angle{BAC}$, $AE\\perp BC$ at $E$. Prove that $\\angle{DAE}=\\dfrac{1}{2}(\\angle{B}\u2212\\angle{C})$. 2. There are four points $A$, $B$, $C$, $D$ on the plane, such that any three &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=2618\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[9,18],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2618"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2618"}],"version-history":[{"count":5,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2618\/revisions"}],"predecessor-version":[{"id":2624,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2618\/revisions\/2624"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}