Congruence
Answers are for parents and teachers.
1
Δ ABC ≅ Δ DEF. Write the three pairs of equal sides.
AB = DE, BC = EF, CA = FD.
2
Two congruent polygons have corresponding sides 4x + 1 and 2x + 9. Find x and the side.
4x + 1 = 2x + 9, so x = 4 and the side is 17.
3
Two triangles have sides 6, 8, 10 cm and 6, 8, 10 cm. Congruent? Which case? What kind of triangles are they?
Yes, by SSS. Since 6² + 8² = 100 = 10², they are right-angled (Pythagoras, week 9).
4
In Δ ABC, AB = AC. The line AD bisects ∠A (D on BC). Prove Δ ABD ≅ Δ ACD.
AB = AC (given), ∠BAD = ∠CAD (AD bisects ∠A), AD is a common side. So the triangles are congruent by SAS, and BD = DC.
5
Two triangles have angles 40°, 60°, 80°. One has a side of 5 cm between the 40° and 60° angles; the other has a side of 5 cm between the 60° and 80° angles. Congruent?
No. The 5 cm sides are not corresponding sides (they are opposite different angles), so the triangles are similar in shape but not the same size.