http://www.ck12.org Chapter 4. Triangles and Congruence
Guided Practice
- Find the value ofxand the measure of each angle.
- Find the measure ofx.
- True or false: Base angles of an isosceles triangle can be right angles.
Answers:
- Set the angles equal to each other and solve forx.
( 4 x+ 12 )◦= ( 5 x− 3 )◦
15 ◦=xIfx= 15 ◦, then the base angles are 4( 15 ◦)+ 12 ◦, or 72◦. The vertex angle is 180◦− 72 ◦− 72 ◦= 36 ◦.
- The two sides are equal, so set them equal to each other and solve forx.
2 x− 9 =x+ 5
x= 14- 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.
Interactive Practice
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/113051