Class 9 Triangles (Congruence) — practice questions with answers
Geometry — Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which criterion proves congruence when three sides of one triangle equal three sides of another?
ASAS
BSSS
CASA
DRHS
Show answer
Answer: B) SSS
SSS = Side-Side-Side. When all three pairs of corresponding sides are equal, the triangles are congruent.
2. Two triangles are congruent only if their corresponding sides and corresponding ______ are all equal. Which word completes this statement?
Aangles
Bareas
Cperimeters
Dmedians
Show answer
Answer: A) angles
Congruence means corresponding sides AND corresponding angles are all equal.
3. If two angles and one side of a triangle equal two angles and the corresponding side of another triangle, they are congruent. This rule (when the side is non-included) is called:
ASSS
BAAS
CSAS
DRHS
Show answer
Answer: B) AAS
AAS (Angle-Angle-Side) uses two angles and a non-included side. It follows from ASA because the third angle is fixed by the angle-sum property.
4. In an isosceles right triangle, the equal angles (other than the right angle) each measure how many degrees?
A49
B41
C90
D45
Show answer
Answer: D) 45
One angle is 90°. The other two are equal: 90 + 2x = 180 → x = 45°.
5. Two sides of a triangle measure 12 cm and 5 cm. Which of the following cannot be the length of the third side?
A8 cm
B10 cm
C16 cm
D18 cm
Show answer
Answer: D) 18 cm
Third side must satisfy 7 < x < 17 (since |12 − 5| = 7 and 12 + 5 = 17). 18 lies outside this range, so it cannot be the third side.