Let’s analyze each statement and determine whether it is true<\/strong> or false<\/strong>, with explanations.<\/p>\n\n\n\n \u2705 True<\/strong> \u274c False<\/strong> \u2705 True<\/strong> \u274c False<\/strong> \u2705 True<\/strong> 1. Though there are two ways in which we classify triangles, we often name a triangle using both its side length and angle measure classifications (e.g., an obtuse isosceles triangle). Given this, answer true or false to the following statements. If the statement is true, draw an example of the triangle. If the statement is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-220492","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=220492"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220492\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n1. A triangle can have exactly 2 acute angles.<\/strong><\/h3>\n\n\n\n
Explanation<\/strong>:
A triangle must have exactly three interior angles<\/strong> that sum to 180\u00b0<\/strong>. An acute angle<\/strong> is an angle less than 90\u00b0.
If two angles are acute (e.g., 60\u00b0 and 50\u00b0), the third angle would be 70\u00b0, which is also acute. But we want exactly<\/strong> two acute angles.
So, if we have two acute angles (e.g., 60\u00b0 and 25\u00b0), the third angle would be 95\u00b0, which is obtuse<\/strong>.
Hence, a triangle can have exactly two acute angles<\/strong> when the third is obtuse or right.<\/p>\n\n\n\n
\n\n\n\n2. A triangle can have an obtuse angle and a right angle.<\/strong><\/h3>\n\n\n\n
Explanation<\/strong>:
A triangle can have only one angle<\/strong> greater than or equal to 90\u00b0, because the sum of all three angles must be 180\u00b0<\/strong>.
A right angle<\/strong> is 90\u00b0, and an obtuse angle<\/strong> is greater than 90\u00b0<\/strong>.
So, 90\u00b0 + any obtuse angle (>90\u00b0) would exceed 180\u00b0, which is not possible<\/strong>.
Therefore, a triangle cannot<\/strong> have both an obtuse and a right angle.<\/p>\n\n\n\n
\n\n\n\n3. A triangle can be scalene and right.<\/strong><\/h3>\n\n\n\n
Explanation<\/strong>:
A scalene triangle<\/strong> has no equal sides or angles<\/strong>.
A right triangle<\/strong> has one 90\u00b0 angle<\/strong>.
A triangle can have one right angle and two other unequal acute angles with all three sides of different lengths.
Example: A triangle with angles 90\u00b0, 60\u00b0, and 30\u00b0 and side lengths 3, 4, 5 is a classic example.<\/p>\n\n\n\n
\n\n\n\n4. A triangle can be equilateral and obtuse.<\/strong><\/h3>\n\n\n\n
Explanation<\/strong>:
An equilateral triangle<\/strong> has three equal sides and three equal angles<\/strong>, each measuring 60\u00b0<\/strong>.
Since all the angles are 60\u00b0, they are all acute<\/strong>, not obtuse.
Therefore, an equilateral triangle cannot be<\/strong> obtuse.<\/p>\n\n\n\n
\n\n\n\n5. A triangle can be isosceles and right.<\/strong><\/h3>\n\n\n\n
Explanation<\/strong>:
An isosceles triangle<\/strong> has two equal sides<\/strong> and two equal angles<\/strong>.
A right triangle<\/strong> has one angle of 90\u00b0<\/strong>.
If a triangle has one right angle and the other two angles are 45\u00b0 each, it’s an isosceles right triangle<\/strong>.
So, yes \u2014 such a triangle is possible (e.g., a triangle with angles 45\u00b0, 45\u00b0, 90\u00b0).<\/p>\n\n\n\n
\n\n\n\nSummary Table:<\/h3>\n\n\n\n
Statement<\/th> True\/False<\/th> Explanation Summary<\/th><\/tr><\/thead> A triangle can have exactly 2 acute angles.<\/td> \u2705 True<\/td> Third angle can be right or obtuse.<\/td><\/tr> A triangle can have an obtuse angle and a right angle.<\/td> \u274c False<\/td> Sum would exceed 180\u00b0.<\/td><\/tr> A triangle can be scalene and right.<\/td> \u2705 True<\/td> Unequal sides with a 90\u00b0 angle is possible.<\/td><\/tr> A triangle can be equilateral and obtuse.<\/td> \u274c False<\/td> Equilateral triangles have only 60\u00b0 angles.<\/td><\/tr> A triangle can be isosceles and right.<\/td> \u2705 True<\/td> 45\u00b0-45\u00b0-90\u00b0 triangle is valid.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n ![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner6-89.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"