Use isosceles and equilateral triangles Section 4-8

Isosceles Triangles Base angle Base angle BASE ANGLE THEOREM… If two sides of a triangle are congruent, then the base angles are also congruent. Base angles are the angles at the ends of the 2 congruent segments, or opposite of the congruent sides. So, in the diagram angles B and C are congruent. There are two congruent sides in an isosceles triangle and two congruent angles. Base angle Base angle

Converse to the Base Angles Theorem If two angles in a triangle are congruent, then the triangle is an isosceles triangle. That means that the 2 sides of the triangles are also congruent.

Equilateral Triangles All of the sides and angles should be congruent. The angles in an equilateral triangle always equal 60o. If it is an equilateral triangle, then it is also equiangular. Converse of Equilateral Triangle Theorem If the triangle is equiangular, then the triangle is equilateral.

Example 1 This is an isosceles triangle, so the 2 sides are congruent…

Example 2 This is an isosceles triangle, so the 2 angles are congruent… 9x = 72 x = 8

Example 3 x + x + 102 = 180 2x + 102 = 180 2x = 78 x = 39

Example 4 The sum of the interior angles is 180… x + 7 = 55 x = 48 55 + 55 + y = 180 110 + y = 180 y = 170

Example 5 Triangle DEG is equilateral, therefore the angles are each 60 degrees. X=60

What are all of the missing angles?

Example 6 GIVEN ANGLE G IS CONGRUENT TO ANGLE J TRIANGLE FGH IS CONGRUENT TO TRIANGLE FJI CPCTC

VERTICAL ANGLE THEOREM GIVEN GIVEN VERTICAL ANGLE THEOREM TRIANGLE AEC IS CONGRUENT TO TRIANGLE BEC CPCTC BASE ANGLE THEOREM

Assignment #46 Page 267 #4-10 even #14-20 even #11 #21 DUE TOMORROW!! I WILL COLLECT IT AT THE BEGINNING OF THE PERIOD! Assignment #46 Page 267 #4-10 even #14-20 even #11 #21 PRINT THE CH. 4 TEST STUDY GUIDE! CLASS THAT BRINGS THE MOST GETS CANDY!!