Congruent & Similar Triangles: The Four Conditions — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 9 · Geometry of 2D Shapes

Congruent & Similar Triangles: The Four Conditions

MEMORANDUM

Name:

Class:

Date:

Mark

/ 15

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Name the four conditions for congruent triangles.
(4)
SSS, SAS, AAS and RHS✓✓✓✓ (4)
2
Why is AAA not a congruency condition?
(2)
Equal angles fix only the shape, not the size — that gives similarity, not congruency.✓✓ (2)
3
In SAS, where must the equal angle be?
(1)
Between the two equal sides (the included angle).✓ (1)
4
Which condition applies only to right-angled triangles?
(1)
RHS✓ (1)
5
If △ABC ≡ △PQR, which side equals BC?
(1)
QR (B pairs with Q and C with R)✓ (1)
6
If △ABC ≡ △PQR, which angle equals Â?
(1)
P̂✓ (1)
7
△ABC ||| △DEF with AB = 3, DE = 9 and BC = 4. Find EF.
(2)
Scale factor 3 → EF = 12✓✓ (2)
8
The two triangles below are drawn to the same scale. Determine whether they are similar, giving a reason, and write down the scale factor from the smaller to the larger.
(3)
9 ÷ 6 = 1,5; 12 ÷ 8 = 1,5; 15 ÷ 10 = 1,5 — all three pairs of corresponding sides are in the same ratio, so yes, the triangles are similar, with scale factor 1,5✓✓✓ (3)

TOTAL: 15 marks