Three pairs of equal sides give the SSS congruence rule in ΔABC and ΔDEF, and the angle opposite the longest side is the largest, so this Class 9 sheet opens with the congruence test and the angle-size rule. The answers record 180° and 70° among later results.
Key Takeaways
Equal sides line up under the SSS rule (Q1).
The angle opposite the longest side is the largest (Q2).
Q3 records 180° as the sum of the angles.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.In ΔABC and ΔDEF, if AB = DE, BC = EF and AC = DF, then the congruence rule used is
(a) SAS(b) SSS(c) ASA(d) RHS
2.In a triangle, the angle opposite to the longest side is
(a) The smallest(b) The largest(c) Always 90°(d) Always 60°
3.The sum of the angles of a triangle is
(a) 90°(b) 180°(c) 270°(d) 360°
4.In an isosceles triangle ABC with AB = AC, the angles opposite to the equal sides are
(a) Equal(b) Supplementary(c) Complementary(d) Not related
5.In ΔABC, if ∠A = 50° and ∠B = 60°, then ∠C is
(a) 50°(b) 60°(c) 70°(d) 80°
6.The measure of each angle of an equilateral triangle is
(a) 45°(b) 60°(c) 90°(d) 120°
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.In ΔABC, if AB = AC and ∠B = 70°, find ∠C.
8.State the angle-sum property of a triangle.
9.In a right triangle, one acute angle is 40°. Find the other acute angle.
10.Which congruence rule is used for two right triangles whose hypotenuse and one side are equal?
11.In ΔABC, if AB = BC, which two angles are equal?
12.An exterior angle of a triangle is 110° and one of its interior opposite angles is 60°. Find the other interior opposite angle.
13.Two angles of a triangle are 45° and 55°. Find the third angle.
14.In an isosceles triangle, the vertical angle is 40°. Find the measure of each base angle.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The angles of a triangle are in the ratio 2 : 3 : 4. Find the measure of each angle.
16.In ΔABC, ∠A = 2∠B and ∠C = 3∠B. Find the measure of each angle of the triangle.
17.The angles of a triangle are (x + 10)°, (2x - 10)° and 3x°. Find the value of x and the measure of each angle.
18.An isosceles triangle has a perimeter of 32 cm and each of its equal sides is 12 cm. Find the length of the base.
19.In an isosceles triangle, each base angle is twice the vertical angle. Find all the angles of the triangle.
20.A triangular piece of land has sides of lengths 7 m, 24 m and 25 m. Check whether the angle opposite the 25 m side is a right angle.
Answer Key
1. b) SSS
2. b) The largest
3. b) 180°
4. a) Equal
5. c) 70°
6. b) 60°
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
Which congruence rule applies when all three pairs of sides are equal?
SSS, option (b) in this worksheet (Q1).
Which angle lies opposite the longest side?
The largest angle, option (b) in this worksheet (Q2).
What is the sum of the angles of a triangle?
180°, option (b) in this worksheet (Q3).
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