Triangles Quiz

Two equilateral triangles are such that the ratio of the product of their three sides to their perimeter is the same for both. No side lengths are given. Can we conclude that the two triangles are congruent?

1. Yes, because all equilateral triangles have equal angles
2. Yes, because equal ratios imply equal sides
3. Yes, because the side lengths of both triangles must be equal
4. No, because the ratio does not determine the shape

Answer: (c) Yes, because the side lengths of both triangles must be equal

Which of the following lengths do not represent the lengths of the sides of a right triangle?

1. 12 cm, 16 cm, 20 cm
2. 10 cm, 24 cm, 26 cm
3. 16 cm, 30 cm, 34 cm
4. 18 cm, 24 cm, 28 cm

Answer: (d) 18 cm, 24 cm, 28 cm

In the given figure, DEF is a triangle whose side DF is produced to G. FH and DH are the bisectors of ∠EFG and ∠EDG respectively. If ∠DEF = 32° and DF = FH, then ∠DHF equals

1. 17°
2. 16°
3. 18°
4. 19°

Answer: (b) 16°

ABCD is a parallelogram as shown in the figure. If AB = 2AD and P is the mid-point of AB, then ∠CPD is equal to

1. 90°
2. 145°
3. 180°
4. 270°

Answer: (a) 90°

Which pf the following statements are correct? Statement 1: Two triangles are said to be congruent, if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other. Statement 2: Two triangles are congruent if two sides and the included angle of one triangle is equal to the corresponding two sides and included angle of the other.

1. Only statement 1
2. Only statement 2
3. Both statement 1 and 2
4. Neither statement 1 and statement 2

Answer: (b) Only statement 2

If one angle of a triangle is 60°and the other two angles are in the ratio 1:2, find the angles.

1. 40°,60°,80°
2. 30°,60°,90°
3. 20°,60°,100°
4. 50°,60°,70°

Answer: (a) 40°,60°,80°

If PQ = PT and ∠TPS = ∠QPR, then what is the ΔPRS?

1. isosceles
2. Equilateral
3. Right angle triangle
4. None

Answer: (a) isosceles

If the bisector of the vertical angle of a triangle bisects the base of the triangle then the triangle is

1. Scalene triangle
2. Equilateral
3. Right angle triangle
4. isosceles triangle.

Answer: (d) isosceles triangle.

In the given congruent triangles under the ASA rule, find the values of x and y, if ΔPQR ≅ ΔSTU.

1. x = 90°, y = 30°
2. x = 60°, y = 30°
3. x = 30°, y = 90°
4. x = 45°, y = 45°

Answer: (c) x = 30°, y = 90°

The triangles shown in the figure below are congruent under RHS congruence criteria. Is this statement true?

1. Yes, because the triangles satisfy the RHS congruence rule
2. No, because the hypotenuse is not equal
3. No, because the right angles are not at the same vertex
4. Yes, because their areas are equal

Answer: (a) Yes, because the triangles satisfy the RHS congruence rule