Grade 9 : Mathematics - 7. Triangles (Set 3)

Question 1

In an isosceles triangle ABC, $AB = AC$ and $\angle B = 65^\circ$.

What is the measure of $\angle A$?

Accepted Answer

A) $50^\circ$

Answer

B) $65^\circ$

Answer

C) $40^\circ$

Answer

D) $55^\circ$

Question 2

In $ riangle PQR$, the lengths of two sides are $PQ = 7cm$ and $QR = 5cm$.

Which of the following CANNOT be the length of side PR?

Accepted Answer

D) 12 cm

Answer

A) 3 cm

Answer

B) 4 cm

Answer

C) 11 cm

Question 3

Given that $ riangle ABC \cong riangle FDE$, with $AB = 6cm$, $\angle B = 50^\circ$, and $\angle A = 70^\circ$.

Which of the following statements is true?

Accepted Answer

A) $FD = 6cm$ and $\angle D = 50^\circ$

Answer

B) $FD = 6cm$ and $\angle E = 60^\circ$

Answer

C) $DE = 6cm$ and $\angle D = 70^\circ$

Answer

D) $DE = 6cm$ and $\angle F = 50^\circ$

Question 4

Line $AD \perp BC$ inside $ riangle ABC$, and AD bisects $\angle BAC$.

If $AB = 3x - 2$ and $AC = x + 8$, find the value of $x$.

Accepted Answer

B) 5

Answer

A) 3

Answer

C) 4

Answer

D) 6

Question 5

In $ riangle XYZ$, the angle measures are given as $\angle X = 40^\circ$ and $\angle Y = 80^\circ$.

Which side of the triangle is the longest?

Accepted Answer

C) XZ

Answer

A) XY

Answer

B) YZ

Answer

D) Cannot be determined

Question 6

Right-angled triangle ABC with $\angle B = 90^\circ$, where point $D$ is the midpoint of hypotenuse AC.

What is the relationship between length BD and hypotenuse AC?

Accepted Answer

A) $BD = \frac{1}{2}AC$

Answer

B) $BD = AC$

Answer

C) $BD = 2AC$

Answer

D) $BD = \frac{1}{3}AC$

Question 7

Points $E$ and $F$ are midpoints of sides AB and AC of $ riangle ABC$.

If $EF = 4.5cm$, find the length of side BC.

Accepted Answer

B) 9 cm

Answer

A) 4.5 cm

Answer

C) 13.5 cm

Answer

D) 6 cm

Question 8

In $ riangle LMN$, the interior angles are given by $\angle L = 3x$, $\angle M = 2x - 10^\circ$, and $\angle N = x + 10^\circ$.

Which side of $ riangle LMN$ is the shortest?

Accepted Answer

A) LM

Answer

B) MN

Answer

C) LN

Answer

D) All sides are equal

Question 9

In $ riangle ABC$, $AB = AC$. The angle bisectors of $\angle B$ and $\angle C$ intersect at point $O$.

If $\angle A = 40^\circ$, find the measure of $\angle BOC$.

Accepted Answer

A) $110^\circ$

Answer

B) $120^\circ$

Answer

C) $140^\circ$

Answer

D) $100^\circ$

Question 10

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

Accepted Answer

C) AAA

Answer

A) SSS

Answer

B) SAS

Answer

D) RHS

Question 11

Point $S$ is any point on side QR of $ riangle PQR$.

Which inequality always holds true?

Accepted Answer

A) $PQ + QR + RP > 2 PS$

Answer

B) $PQ + QR < PS$

Answer

C) $PS + SR < PR$

Answer

D) $PQ + PR < 2 PS$

Question 12

In $ riangle ABC$, median AD is drawn from vertex $A$ to side BC.

Which of the following relations is correct regarding the sum of sides $AB + AC$?

Accepted Answer

A) $AB + AC > 2 AD$

Answer

B) $AB + AC < 2 AD$

Answer

C) $AB + AC = 2 AD$

Answer

D) $AB + AC = AD$

Question 13

Quadrilateral ABCD with diagonals AC and BD.

Which statement correctly compares the perimeter of quadrilateral ABCD to the sum of its diagonals?

Accepted Answer

A) $AB + BC + CD + DA > AC + BD$

Answer

B) $AB + BC + CD + DA < AC + BD$

Answer

C) $AB + BC + CD + DA = AC + BD$

Answer

D) $AB + CD = AC + BD$

Question 14

In $ riangle ABC$, $AB = 5cm$, $BC = 8cm$, and $AC = 7cm$.

Which option shows the interior angles arranged in strictly ascending order?

Accepted Answer

A) $\angle C < \angle B < \angle A$

Answer

B) $\angle A < \angle B < \angle C$

Answer

C) $\angle B < \angle C < \angle A$

Answer

D) $\angle C < \angle A < \angle B$

Question 15

In $ riangle ABC$, $\angle B = 90^\circ$ and $D$ is the midpoint of BC. Given $AB = 6cm$ and $BC = 8cm$.

Calculate the length of median AD.

Accepted Answer

B) $2\sqrt{13}cm$

Answer

A) 5 cm

Answer

C) $\sqrt{37}cm$

Answer

D) 10 cm

Question 16

To prove $ riangle ABC \cong riangle DFE$ using the SAS criterion, you are given $AB = FD$ and $\angle A = \angle D$.

Which additional pair of sides must be equal?

Accepted Answer

B) $AC = DE$

Answer

A) $BC = EF$

Answer

C) $AC = EF$

Answer

D) $\angle B = \angle F$

Question 17

An isosceles triangle ABC has $AB = AC = 13cm$. The altitude AD drawn from $A$ to base BC measures 12 cm.

Find the perimeter of $ riangle ABC$.

Accepted Answer

A) 36 cm

Answer

B) 32 cm

Answer

C) 30 cm

Answer

D) 24 cm

Question 18

In $ riangle ABC$, $P$ and $Q$ are points on AB and AC respectively such that $PQ \parallel BC$.

If $AP = 3cm$, $PB = 6cm$, and $AQ = 4cm$, find the length of QC.

Accepted Answer

A) 8 cm

Answer

B) 6 cm

Answer

C) 12 cm

Answer

D) 10 cm

Question 19

In $ riangle ABC$, $\angle A = 50^\circ$. The internal bisector of $\angle B$ and the external bisector of $\angle C$ meet at point $E$.

What is the measure of $\angle BEC$?

Accepted Answer

A) $25^\circ$

Answer

B) $50^\circ$

Answer

C) $65^\circ$

Answer

D) $40^\circ$

Question 20

In $ riangle ABC$, AD is the bisector of $\angle BAC$ meeting BC at point $D$.

If $AB = 8cm$, $AC = 12cm$, and $BD = 4cm$, find the length of DC.

Accepted Answer

A) 6 cm

Answer

B) 8 cm

Answer

C) 5 cm

Answer

D) 10 cm

Grade 9 : Mathematics - 7. Triangles (Set 3)