Use congruent triangles to find missing sides and angles

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ari wants to say ∠B = ∠E for the two triangles on the card. Which justification works?

   • CPCTC alone: the three side pairs match, so the angle pairs match
   • SSS proves △ABC ≅ △DEF, then ∠B = ∠E by CPCTC
   • Nothing yet: no pair of angles is marked equal
   • ∠B and ∠E look the same size in the picture
2. 2.

   Esme says BC = EF because all three angle pairs match. Which reply is right?

   • Proved: matching angles are corresponding parts, so BC = EF by CPCTC
   • Not proved: equal angles only make similar triangles
   • Proved if both triangles are drawn the same size
   • Proved: AAA is a congruence rule, so BC = EF by CPCTC
3. 3.

   Jun wants to say AB = CB. Which justification works?

   • Not enough: one pair of sides is marked equal
   • BD = BD (shared); SAS gives △ABD ≅ △CBD, so AB = CB
   • ASA gives △ABD ≅ △CBD, so AB = CB by CPCTC
   • ∠ADB = ∠CDB, so the sides opposite are equal by CPCTC
4. 4.

   Luz needs the reason for line 4 of a proof. Which reason is right?

   • Vertical angles are equal
   • Linear pair: the two angles add up to 180°
   • CPCTC: the angles are corresponding parts
   • Given: the picture shows them equal
5. 5.

   Milo needs the reason for line 2 of a proof. Which reason is right?

   • Definition of midpoint: B is halfway along AC
   • Given: two tick marks show they are equal
   • CPCTC: the sides are corresponding parts
   • Reflexive property: a segment equals itself
6. 6.

   A proof has shown triangle ABC ≅ triangle DEF by SAS. The next line says ∠C = ∠F. Noah needs the reason for the next line after proving a congruence. Which reason is right?

   • CPCTC: corresponding parts of congruent triangles are congruent
   • Given: the angles are marked in the picture
   • Vertical angles are equal
   • SAS: the rule that was just used to show the triangles congruent
7. 7.

   not to scale. Pia wants to prove △ABC ≅ △DEF by SAS. Which one more fact is needed?

   • AC = EF, which pairs the wrong sides
   • AC = DF, next to the marked angle
   • BC = EF, which makes SSA, not a rule
   • ∠B = ∠E, which makes ASA, not SAS
8. 8.

   Ren wants to prove △PQR ≅ △XYZ by ASA. Which one more fact is needed?

   • PQ = XY, between the two marked angles
   • PR = XZ, which makes AAS, not ASA
   • PQ = XZ, which pairs the wrong sides
   • ∠R = ∠Z, because three angles are enough
9. 9.

   Triangles ABC and DEF, not to scale. Tala wants to prove △ABC ≅ △DEF by SSS. Which one more fact is needed?

   • ∠B = ∠E, which makes SAS, not SSS
   • AC = DF
   • ∠A = ∠D, which makes SSA, not a rule
   • AC = DE, which pairs the wrong sides
10. 10.

    Zee wants to prove △ABC ≅ △DEF by HL. Which one more fact is needed?

    • AC = DF, a pair of legs
    • ∠C = ∠F, the right angles
    • BC = DE, a leg and a hypotenuse
    • ∠A = ∠D, which makes AAS, not HL