CK-12 Geometry Concepts

4.10. Isosceles Triangles http://www.ck12.org

Guided Practice

1. Find the value ofxand the measure of each angle.


2. Find the measure ofx.


3. True or false: Base angles of an isosceles triangle can be right angles.

Answers:

1. Set the angles equal to each other and solve forx.

( 4 x+ 12 )◦= ( 5 x− 3 )◦

15 ◦=x

Ifx= 15 ◦, then the base angles are 4( 15 ◦)+ 12 ◦, or 72◦. The vertex angle is 180◦− 72 ◦− 72 ◦= 36 ◦.

2. The two sides are equal, so set them equal to each other and solve forx.

2 x− 9 =x+ 5

x= 14

3. This statement is false. Because the base angles of an isosceles triangle are congruent, if one base angle is a right
   angle then both base angles must be right angles. It is impossible to have a triangle with two right (90◦) angles. The
   Triangle Sum Theorem states that the sum of the three angles in a triangle is 180◦. If two of the angles in a triangle
   are right angles, then the third angle must be 0◦and the shape is no longer a triangle.

Practice

Find the measures ofxand/ory.

1.

2.

3.

4.

5.

Determine if the following statements are true or false.

6. Base angles of an isosceles triangle are congruent.


7. Base angles of an isosceles triangle are complementary.


8. Base angles of an isosceles triangle can be equal to the vertex angle.


9. Base angles of an isosceles triangle are acute.

Complete the proofs below.

10.Given: Isosceles 4 CIS, with base angles^6 Cand^6 SIOis the angle bisector of^6 CISProve:IOis the perpen-

dicular bisector ofCS

11.Given: Isosceles 4 ICSwith^6 Cand^6 SIOis the perpendicular bisector ofCSProve:IOis the angle bisector

of^6 CIS