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Q1. In ΔABC shown below, ADBC, BEAC and AD = BE. Prove that AE = BD.  

Solution

Given :ADBC, BEAC and AD = BE   To prove:AE = BD   Proof:   ADB = BEA(right angles)   AB = AB(common)   AD = BE(given)   Thus, ABD BAE(By RHS congruence rule).   Hence,BD = AE(Since, corresponding parts of congruent triangles are equal)        

Q2. 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.

• 1) None of the above
• 2) 45 cm , 9 cm
• 3) 5 cm, 9 cm
• 4) 9 cm, 5 cm

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.

Q3. Given below are measurements of some parts of pair of triangles which of the pair of two triangles are congruent to each other.

• 1)
• 2)
• 3)
• 4)

Solution

Q4. In the adjoining figure, if AB  = PQ and BC = CQ, then find the measure of angle CPQ.

• 1) 90^o
• 2) 80^o
• 3) 60^o
• 4) 30^o

Solution

In triangles ABC and PQC, we have: AB = PQ BC = CQ B = Q Thus, triangles ABC and PQC are congruent. Therefore, BAC = CPQ Now, applying angle sum property in triangle ABC, we get, BAC = 180^o - 70^o- 30^o = 80^o Therefore, CPQ = 80^o

Q5. In ∆STU and ∆PQR, ST = 5, TU = 6 and SU = 7. What is the measure of RP?

• 1) 5
• 2) Data insufficient
• 3) 7
• 4) 6

Solution

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

Q6. Given below are two triangles ABD and CBD. AD = CD and ∠3 = ∠4. Prove that DB bisects ∠ABC.        

Solution

     

Q7. Name all the corresponding parts of the congruent figures given below:

Solution

Given that, both the figures are congruent.Corresponding sides: OP WX; OR UX; QR UV; QP VW Corresponding vertices: O X; P W; Q V; R U Corresponding angles: