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 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.

Triangles and are isosceles. Angle has a measure of 18 degrees, and angle has a measure of 48 degrees. Find the measure of angle .

Here are some statements about two zigzags. Put them in order to prove figure is congruent to figure .

Two figures, A B C and D E F, each composed of two line segments that share an endpoint . A B slants upward and to the left and B C slants upward and to the right. Figure D E F is below and to the right of figure A B C. D E slants upward and to the left and E F slants upward and slightly to the left. B C and E F have one tick mark. A B and D E have two tick marks. Angles B and E marked equal.

• 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 .

Match each statement using only the information shown in the pairs of congruent triangles.