Grade 9 : Mathematics - 7. Triangles (Set 2)

Question 1

In $ riangle ABC$ and $ riangle PQR$, it is given that $AB = PQ$, $BC = QR$, and $\angle B = \angle Q = 50^\circ$.

By which congruence criterion are $ riangle ABC$ and $ riangle PQR$ congruent?

Accepted Answer

A) SAS

Answer

B) ASA

Answer

C) SSS

Answer

D) RHS

Question 2

In $ riangle ABC$, $AB = AC$ and $\angle B = 70^\circ$.

What is the measure of $\angle A$?

Accepted Answer

A) $40^\circ$

Answer

B) $50^\circ$

Answer

C) $70^\circ$

Answer

D) $110^\circ$

Question 3

Which of the following is NOT a valid congruence criterion for triangles?

Accepted Answer

C) AAA

Answer

A) SAS

Answer

B) ASA

Answer

D) SSS

Question 4

In $ riangle PQR$, the angles are $\angle P = 60^\circ$ and $\angle Q = 80^\circ$.

Which side of $ riangle PQR$ is the longest?

Accepted Answer

C) PR

Answer

A) PQ

Answer

B) QR

Answer

D) Cannot be determined

Question 5

In right-angled triangles $ riangle ABC$ and $ riangle DEF$, hypotenuse $AC = DF$ and side $AB = DE$.

Which congruence criterion establishes that $ riangle ABC \cong riangle DEF$?

Accepted Answer

B) RHS

Answer

A) SAS

Answer

C) SSS

Answer

D) ASA

Question 6

In $ riangle ABC$, $\angle A = 50^\circ$ and $\angle B = 60^\circ$.

Find the measure of $\angle C$.

Accepted Answer

C) $70^\circ$

Answer

A) $50^\circ$

Answer

B) $60^\circ$

Answer

D) $80^\circ$

Question 7

Given statement: $ riangle ABC \cong riangle FDE$.

Which of the following side equalities is true based on CPCT?

Accepted Answer

C) $AC = FE$

Answer

A) $AB = DE$

Answer

B) $BC = EF$

Answer

D) $AB = EF$

Question 8

In an isosceles triangle XYZ, $XY = XZ$. If vertex angle $\angle X = 80^\circ$.

What is the measure of base angle $\angle Y$?

Accepted Answer

A) $50^\circ$

Answer

B) $80^\circ$

Answer

C) $100^\circ$

Answer

D) $40^\circ$

Question 9

Is it possible to form a triangle with side lengths 4 cm, 7 cm, and 12 cm?

Accepted Answer

B) No

Answer

A) Yes

Answer

C) Depends on the interior angles

Answer

D) Only if it is right-angled

Question 10

In $ riangle ABC$, line segment $AD \perp BC$ such that AD bisects BC.

What type of triangle is $ riangle ABC$?

Accepted Answer

B) Isosceles with $AB = AC$

Answer

A) Scalene

Answer

C) Right-angled only

Answer

D) Equilateral only

Question 11

If all three angles of a triangle are equal to each other, what is the measure of each angle?

Accepted Answer

B) $60^\circ$

Answer

A) $45^\circ$

Answer

C) $90^\circ$

Answer

D) $30^\circ$

Question 12

In $ riangle ABC$ and $ riangle DEF$, $\angle A = \angle D = 90^\circ$, $AB = DE$, and $\angle B = \angle E = 45^\circ$.

By which criterion are these triangles congruent?

Accepted Answer

A) ASA

Answer

B) SSS

Answer

C) RHS

Answer

D) AAA

Question 13

The perimeter of an equilateral triangle is 36 cm.

What is the length of each side?

Accepted Answer

C) 12 cm

Answer

A) 6 cm

Answer

B) 9 cm

Answer

D) 18 cm

Question 14

In $ riangle ABC$, it is given that $\angle A > \angle B$.

Which inequality relation between sides BC and AC is correct?

Accepted Answer

A) $BC > AC$

Answer

B) $BC < AC$

Answer

C) $BC = AC$

Answer

D) $BC \le AC$

Question 15

Two interior angles of a triangle measure $35^\circ$ and $65^\circ$.

What type of triangle is this according to its angle measures?

Accepted Answer

C) Acute-angled

Answer

A) Right-angled

Answer

B) Obtuse-angled

Answer

D) Equilateral

Question 16

In $ riangle LMN$, $LM = LN$. The angle $\angle L = 100^\circ$.

Find the measure of $\angle M$.

Accepted Answer

A) $40^\circ$

Answer

B) $80^\circ$

Answer

C) $50^\circ$

Answer

D) $100^\circ$

Question 17

Two side lengths of a triangle are $AB = 5cm$ and $BC = 8cm$.

The length of side AC must strictly be greater than:

Accepted Answer

B) 3 cm

Answer

A) 2 cm

Answer

C) 5 cm

Answer

D) 13 cm

Question 18

Given that $ riangle ABC \cong riangle PQR$ by the SSS criterion.

Which side relation is correct?

Accepted Answer

C) $AC = PR$

Answer

A) $AB = QR$

Answer

B) $BC = PQ$

Answer

D) $AB = PR$

Question 19

In a right-angled triangle, one acute angle measures $38^\circ$.

What is the measure of the other acute angle?

Accepted Answer

B) $52^\circ$

Answer

A) $42^\circ$

Answer

C) $62^\circ$

Answer

D) $142^\circ$

Question 20

In $ riangle ABC$, points $E$ and $F$ are the midpoints of sides AB and AC respectively. The base $BC = 14cm$.

Find the length of line segment EF.

Accepted Answer

A) 7 cm

Answer

B) 14 cm

Answer

C) 28 cm

Answer

D) 10.5 cm

Grade 9 : Mathematics - 7. Triangles (Set 2)