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Q1. Which of the following is not a congruence criteria?

• SSS
• SAS
• ASS
• ASA

Solution

ASS is not a congruence criteria followed to check the congruence of two similar triangle. 

Q2. Which one of the following congruency condition is not possible for two triangles to be congruent:

• SSS
• SAS
• ASA
• AAA

Solution

AAA congruency criteria is not possible because equiangular triangles will have just same shape but not the same size.

Q3. In an Isosceles triangle, perpendicular drawn to the unequal side divide the triangle into two ______ triangles.

• Isosceles
• Congruent
• Equilateral
• Equal

Solution

In isosceles triangle, the perpendicular drawn to unequal side bisect it at right angles. Thus, by SAS congruency condition, two triangles are congruent.

Q4. The angle bisector of an angle divides the angle into two ______ angles.

• Congruent
• Right
• Obtuse
• Acute

Solution

Congruent

Q5. If one side and hypotenuse of one right angled triangle is equal to corresponding side and hypotenuse of the other triangle, they are said to be congruent by ______ congruency.

• SSS
• SAS
• RHS
• ASA

Solution

This is RHS congruence condition.

Q6. Triangle ABC is congruent to Triangle PQR, if area of triangle ABC is 42 square unit, then area of the triangle PQR is

• 24 square units
• 84 square units
• 42 square units
• 21 square units

Solution

If two triangles are congruent, they are said to be equal in area as well. So, area of triangle PQR = 42 square units

Q7. The dimensions of pairs is triangles are given. Which of the following pair of triangles is congruent?

• (12, 8, 5); (12, 8, 7)
• (7, 8, 9); (9, 8, 7)
• (3, 4, 5); (3, 3, 5)
• (6, 5, 9); (9, 7, 17)

Solution

SSS congruency. Three sides of one triangle are equal to three sides of another triangle. So, the triangles with the dimensions (7, 8, 9); (9, 8, 7) are congruent. 

Q8. In ∆STU and ∆PQR, ST = 5, TU = 6 and SU = 7. What is the measure of RP?

• 5
• 6
• 7
• Data insufficient

Solution

Adequate data is not available. ∆STU ≅ ∆PQR is not given. 

Q9. Rectangles R₁ and R₂ are congruent, R₁ has an area of 45 cm² and length 9 cm. So, R₂ will have length and breadth as _____, respectively.

• 5 cm, 9 cm
• 9 cm, 5 cm
• 45 cm , 9 cm
• None of the above

Solution

Congruent rectangles have corresponding length and breadth equal. Area of R₁ = 45 = 9 × 5 = length × breadth = Area of R₂ ∴ R₂ will have length and breadth as 9 cm and 5 cm, respectively.

Q10. If two triangles are congruent then the perimeter of one triangle is equal to ______ of the other triangle.

• Perimeter
• Area
• Angles
• Sides

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