Side-Angle-Side Triangle Congruence
1) Triangle is isosceles with congruent sides and . Which additional given information is sufficient for showing that triangle is isosceles?
Select all that apply. Write each corresponding letter in the answer box and separate letters with commas.
a) Line is an angle bisector of . b) Angle is congruent to angle .
c) Angle is congruent to angle . d) Angle is congruent to angle .
e) Triangle is congruent to triangle .
2) Tyler has written an incorrect proof to show that quadrilateral is a parallelogram. He knows segments and are congruent. He also knows angles and are congruent. Find the mistake in his proof:
Segment is congruent to itself, so triangle is congruent to triangle by Side-Angle-Side Triangle Congruence Theorem. Since the triangles are congruent, so are the corresponding parts, and so angle is congruent to . In quadrilateral , is congruent to and is parallel to . Since is parallel to , alternate interior angles and are congruent. Since alternate interior angles are congruent, must be parallel to . Quadrilateral must be a parallelogram since both pairs of opposite sides are parallel.
3) Triangles and are isosceles. Angle has a measure of 18 degrees and angle has a measure of 48 degrees. Find the measure of angle .
4) Here are some statements about 2 zigzags. Put them in order to prove figure is congruent to figure .
1. If necessary, reflect the image of figure across to be sure the image of , which we will call , is on the same side of as .
2. must be on ray since both and are on the same side of and make the same angle with it at .
3. Segments and are the same length so they are congruent. Therefore, there is a rigid motion that takes to . Apply that rigid motion to figure .
4. Since points and are the same distance along the same ray from they have to be in the same place.
5. Therefore, figure is congruent to figure .
Write your answer as a list of statement numbers in correct order for the proof, separated by commas.
Match each statement below to one of the pairs of congruent triangles. Write the number of the correct image in the answer box.
5) The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.
6) In the 2 triangles there are 3 pairs of congruent sides.
7) The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.
8) Triangle is congruent to triangle . So, Priya knows that there is a sequence of rigid motions that takes to .
Select all true statements after the transformations. Write each corresponding letter in the answer box and separate letters with commas.
a) Segment coincides with segment . b) Segment coincides with segment .
c) Segment coincides with segment . d) Angle coincides with angle .
e) Angle coincides with angle .