{"id":9019,"date":"2020-12-04T05:51:46","date_gmt":"2020-12-04T00:21:46","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=9019"},"modified":"2020-12-04T14:54:29","modified_gmt":"2020-12-04T09:24:29","slug":"isosceles-triangle-theorems","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/isosceles-triangle-theorems\/","title":{"rendered":"Isosceles Triangle Theorems"},"content":{"rendered":"
An isosceles triangle<\/strong> is a triangle with two congruent sides. Examples:<\/strong><\/p>\n Isosceles Triangle Theorems An isosceles triangle is a triangle with two congruent sides. Theorem: If two sides of a triangle are congruent, the angles opposite them are congruent. Theorem: (converse) If two angles of a triangle are congruent, the sides opposite them are congruent. More Info: When the altitude is drawn in an isosceles triangle, … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"yoast_head":"\n
\nTheorem:<\/strong>
\nIf two sides of a triangle are congruent, the angles opposite them are congruent.
\nTheorem: (converse)<\/strong>
\nIf two angles of a triangle are congruent, the sides opposite them are congruent.
\nMore Info:<\/strong>
\nWhen the altitude is drawn in an isosceles triangle, two congruent triangles are formed, proven by Hypotenuse-Leg.
\n(The congruent legs of the isosceles triangle become the congruent hypotenuses and the altitude becomes a shared leg.)
\nThese congruent<\/strong> triangles make it possible, by use of CPCTC, to conclude that the following statements are true regarding an isosceles triangle:<\/p>\n
\n
\n<\/li>\n
\n<\/li>\n<\/ol>\n
\n
\n
\nSolution:<\/strong>
\nIf two angles of a triangle are congruent, the sides opposite them are congruent.
\nSet: 6x – 8 = 4x + 2
\n2x = 10
\nx = 5
\nNote: The side labeled 2x + 2 is a distracter and is not used in finding x.<\/li>\n
\n
\nSolution:<\/strong>
\nIf two sides of a triangle are congruent, the angles opposite them are congruent.
\nSo m\u22201 = m\u22202 and m\u22203 = 40 degrees.
\n180 – 50 = 130 180 – (40 + 40) = 100
\nm\u22201 = 65 degrees m \u22204 = 100 degrees
\nm\u22202 = 65 degrees<\/li>\n
\nSolution:<\/strong>
\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"