Matching sides and angles of congruent figures

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Ari knows quadrilateral FGHJ is congruent to quadrilateral PQRS, with F↔R, G↔S, H↔P and J↔Q. What is the size of angle Q?

   95
2. 2.

   Bo knows quadrilateral ABCD is congruent to quadrilateral WXYZ, with A↔Y, B↔Z, C↔W and D↔X. What is the size of angle X?

   85
3. 3.

   Esme knows quadrilateral ABCD is congruent to quadrilateral WXYZ, with A↔Y, B↔Z, C↔W and D↔X. What is the size of angle Y?

   110
4. 4.

   Kira knows triangle ABC is congruent to triangle ZXY, with A↔Z, B↔X and C↔Y. What is the perimeter of triangle ZXY?

   67
5. 5.

   Milo knows triangle ABC is congruent to triangle QRS, with A↔S, B↔Q and C↔R. What is the perimeter of triangle QRS?

   82
6. 6.

   Noah knows triangle ABC is congruent to triangle MNP, with A↔N, B↔P and C↔M. What is the perimeter of triangle MNP?

   59
7. 7.

   Pia asks whether a slide, flip or turn can put triangle P exactly onto triangle Q. Is that possible?

   • No: the first sides listed, 6 cm and 10 cm, are different.
   • No: Q looks like P flipped over, which changes the triangle.
   • No: no angles are given, so nobody can tell.
   • Yes: the sides match in pairs (6 and 6, 8 and 8, 10 and 10).
8. 8.

   Ren asks whether a slide, flip or turn can put triangle P exactly onto triangle Q. Is that possible?

   • Yes: all three angles match in pairs.
   • Yes: sliding Q over P lines up the sides.
   • No: the angles match, but Q's sides are twice as long as P's.
   • Yes: the triangles have the same shape, so one fits on the other.
9. 9.

   Tala asks whether a slide, flip or turn can put triangle P exactly onto triangle Q. Is that possible?

   • Yes: two pairs of sides match, 7 and 9.
   • Yes: sliding Q onto P lines up the third sides.
   • Yes: the sides differ by only 1 cm, so one fits on the other.
   • No: the third sides differ, 12 cm and 13 cm.
10. 10.

    Zee asks whether a slide, flip or turn can put triangle P exactly onto triangle Q. Is that possible?

    • Yes: two angles and the side between them match, which fixes the whole triangle.
    • No: Q looks like P flipped over, which changes the triangle.
    • No: the third angle and two sides are not given, so nobody can tell.
    • No: the first angles listed, 50° and 60°, are different.