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CBSE Class 9  >  Class 9 Test  >  Mathematics (Maths)   >  Test: Properties of Isosceles Triangle - Class 9 MCQ

Properties of Isosceles Triangle - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Properties of Isosceles Triangle (10 Questions)

You can prepare effectively for Class 9 Mathematics (Maths) Class 9 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Properties of Isosceles Triangle". These 10 questions have been designed by the experts with the latest curriculum of Class 9 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Properties of Isosceles Triangle - Question 1
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In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ≅ ΔDEF by the criterion

Detailed Solution: Question 1

Answer: b) AAS

Why:
Both triangles are right-angled (∠B = ∠E = 90°). An acute angle is given equal (∠A = ∠D), and one corresponding side is equal (BC = EF). That’s two angles (one is the right angle) and a non-included side → AAS congruence.

Why not the others:

  • ASA: the given side is not the side included between the two known angles.
  • SAS: only one side is known, not two.
  • SSS: three sides are not given.
 

Test: Properties of Isosceles Triangle - Question 2
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In ΔABC if ∠A = ∠B, then

Detailed Solution: Question 2

Becuase Sides opposite to equal angles are also equal.angle A = angle BBC is opposite to angle A and AC is opposite to angle B.Therefore, AC=BC in triangle ABC.

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Test: Properties of Isosceles Triangle - Question 3
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In the given figure, AB = AC and ∠ACD = 105°, ∠BAC will be

Detailed Solution: Question 3

Step-by-step solution  

  1. In the figure, ∠ACD is given as 105°.
    Since ∠ACD and ∠ACB are on a straight line, they form linear pair
    ∠ACD + ∠ACB = 100º
    ∠ACB = 180° − 105° = 75°

  2. The triangle is isosceles (AB = AC), so the base angles are equal:
    ∠ABC = ∠ACB = 75°

  3. Now, sum of angles in a triangle is 180°:
    ∠ACB + ∠BAC + ∠ABC = 180º
    ∠BAC = 180° − (75° + 75°) = 30°

Test: Properties of Isosceles Triangle - Question 4
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PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. then

Detailed Solution: Question 4

Since ST is parallel to QR and S is on PQ, by the Basic Proportionality Theorem (or Thales' theorem):

PS/SQ = PT/TR

However, since PQ=PR, triangles △PSQ and △PRT are similar due to the AA (Angle-Angle) criterion (one angle is common, and the other angles are corresponding angles formed by the parallel lines).

PS/SQ = PT/TR = 1

PS = PT

Test: Properties of Isosceles Triangle - Question 5
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The altitude of an equilateral triangle of side a to any of its other sides from the opposite vertex is

Detailed Solution: Question 5

This is because in an equilateral triangle, all sides are equal, and the altitude divides the triangle into two 30-60-90 right triangles. In a 30-60-90 triangle, the ratio of the sides opposite to the angles 30°, 60°, and 90° are, respectively.

Test: Properties of Isosceles Triangle - Question 6
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In an isosceles right angled triangle, the measures of the acute angles are​

Detailed Solution: Question 6

In an isosceles right-angled triangle:
- An isosceles triangle has two equal angles.
- A right-angled triangle has a 90° angle.
- In this case, the two acute angles are equal.
- So, each acute angle in an isosceles right-angled triangle will be 45°.
Therefore, the correct answer is C: 45°, 45°.

Test: Properties of Isosceles Triangle - Question 7
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In ΔABC if AB = BC then:

Detailed Solution: Question 7

In triangle ABC with AB = BC:
- Angles A and C are equal (congruent) because the sides opposite them are equal in an isosceles triangle.
- So, the correct answer is:
- Angle A = Angle C (Option C)

Test: Properties of Isosceles Triangle - Question 8
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Pick out the incorrect statement

Detailed Solution: Question 8

The altitudes of a triangle are the line segments drawn from each side of the triangle to the angle opposite that side, such that the line segment is perpendicular to the side it is drawn from. In an isosceles triangle, only the altitudes of the legs of equal length in the triangle are congruent. 

Test: Properties of Isosceles Triangle - Question 9
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If the bisector of the exterior vertical angle of a triangle is parallel to the base, then it is

Detailed Solution: Question 9

∠CAE is the external vertical angle and AD is its bisector.
 
∴ ∠CAD = ∠DAE  .... (i)
 
As, AD || BC
 
∴ ∠CAD = ∠ACB  .... (ii)  (alternate angle)
 
and ∠DAE = ∠ABC  ....(iii)  (corresponding angle)
 
From (i), (ii) and (iii),
 
∠ABC = ∠ACB
 
∴ AC = AB  (opposite sides to equal angles)
 
Hence, ΔABC is isosceles.

Test: Properties of Isosceles Triangle - Question 10
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In triangle PQR, PQ = PR and R = 65°, then P = ?

Detailed Solution: Question 10

By using the theorem,If two sides of a triangle are equal then the opposite angles to the sides are equal.
⇒ if PQ=PR then ∠Q=∠R
in triangle PQR,
⇒ ∠P+∠Q+∠R=180°
⇒ ∠P+∠Q+∠Q=180° (∵∠Q=∠R)
⇒ ∠P+65°+65°=180°
⇒ ∠P+130°=180°
⇒ ∠P=180°-130°
⇒ ∠P=50

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About this Class 9 Practice Test

This test contains 10 MCQs on Properties of Isosceles Triangle with detailed solutions for each question. It is part of the Mathematics (Maths) Class 9 course on EduRev, designed to align with the current Class 9 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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