CONGRUENCE REVISION QUESTIONS

Triangle Congruence Questions

1. In triangle \(ABC\) and triangle \(DEF\), \(AB = DE\), \(BC = EF\), and \(AC = DF\). Are the triangles congruent? State the rule.

2. Prove that two triangles with all sides equal in length are congruent. What congruence rule applies?

3. In triangle \(XYZ\), \(XY = 5\) cm, \(YZ = 7\) cm, \(XZ = 6\) cm. Another triangle \(PQR\) has the same side lengths. Are they congruent?

4. Two triangles have two angles and the included side equal. Which rule applies to prove they are congruent?

5. Triangle \(ABC\) has sides \(AB = AC\) and angle \(B = C\). Is triangle \(ABC\) congruent to triangle \(DEF\) if \(DE = DF\) and angle \(E = F\)?

6. State the four rules of triangle congruence.

7. Are two right-angled triangles congruent if their hypotenuses and one leg are equal?

8. Can the SAS rule be used if the known angle is not between the two known sides?

9. Triangle \(MNP\) and triangle \(QRS\) have \(MN = QR\), \(NP = RS\), and angle \(N = R\). Are they congruent?

10. Explain the difference between SSS and SAS rules.

11. Two triangles have equal corresponding sides. What does this imply?

12. If triangle \(ABC\) has angles \(A = 60^\circ\), \(B = 60^\circ\), and \(C = 60^\circ\), is it congruent to triangle \(DEF\) with the same angles?

13. Can AAA (Angle-Angle-Angle) prove congruence?

14. What congruence rule is best for proving two isosceles triangles are congruent?

15. Draw two triangles where two sides and the included angle are equal. Are they congruent?

16. In the figure below, identify a pair of congruent triangles and state the rule.

17. Can HL (Hypotenuse-Leg) rule be used to prove triangle congruence? When?

18. Which rule can be used to prove congruence of equilateral triangles?

19. Given triangles \(ABC\) and \(DEF\), \(AB = DE\), \(BC = EF\), angle \(B = E\). Prove they are congruent.

20. Describe a real-life situation where triangle congruence is used.

21. Triangle \(PQR\): \(PQ = QR = RP = 5\) cm. Triangle \(XYZ\): same dimensions. Are they congruent?

22. If a triangle is reflected across a line, is it still congruent to its original?

23. Name the congruence rule: Two triangles with all three angles and two sides equal.

24. Why is SSA not a valid congruence rule in general?

25. Can two triangles be congruent if they have the same area and perimeter?

26. Triangle \(ABC\) has \(AB = 7\) cm, angle \(B = 50^\circ\), \(BC = 9\) cm. Another triangle has same specs. Are they congruent?

27. Show that two right triangles with equal hypotenuses and one leg equal are congruent.

28. Triangle \(JKL\) and triangle \(MNO\) have \(JK = MN\), \(KL = NO\), angle \(K = N\). Prove congruence.

29. Are triangles with corresponding equal sides but different orientation congruent?

30. What test is most reliable for proving triangle congruence in constructions?

Answers

1. Yes, by SSS rule.
2. SSS rule applies.
3. Yes, by SSS.
4. SAS rule.
5. Yes, by SAS.
6. SSS, SAS, ASA, and RHS/HL (Right angle-Hypotenuse-Side).
7. Yes, by RHS rule.
8. No, angle must be included for SAS.
9. Yes, SAS rule applies.
10. SSS uses all sides, SAS uses two sides and the included angle.
11. They are congruent.
12. No, AAA only shows similarity.
13. No, AAA is not enough.
14. Usually SAS or SSS.
15. Yes, if all equal, then SSS.
16. By SAS rule.
17. Yes, in right triangles.
18. SSS.
19. Use SAS to prove.
20. Architecture, engineering, bridge design, etc.
21. Yes, by SSS.
22. Yes, reflections preserve congruence.
23. Likely ASA or AAS, not congruent unless angle is included.
24. SSA does not guarantee congruence (Ambiguous case).
25. No, not always.
26. Yes, by SAS.
27. RHS rule applies.
28. SAS rule.
29. Yes, orientation doesn’t affect congruence.
30. SSS or SAS, depending on given information.