Students can Download Maths Chapter 11 Congruency of Triangles Ex 11.2 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka Board Class 8 Maths Chapter 11 Congruency of Triangles Ex 11.2

Question 1.

In the adjoining figure PQRS is a rectangle. Identify the congruent triangles formed by the diagonals.

Answer:

Δ PSR ≅ Δ PQR, Δ POQ ≅ Δ SOR

Δ SPQ ≅ Δ SRQ, Δ POS ≅ Δ QOR

Question 2.

In the figure ABCD is a square. M, N, O & P are the midpoints of sides AB, BC, CD and DA respectively. Identify the congurent triangles.

Answer:

Δ APM ≅ Δ BMD ≅ Δ CNO ≅ Δ DOP

Question 3.

In a triangle ABC, AB = AC. Points G on AB and D on AC are such that AE = AD. Prove that triangles BCD and CBE are congruent.

Answer:

In the figure AB = AC (data)

∴∠ABC = ∠ACB

[Base angles of an isosceles triangle]

AB = AC(data)

AE = AD(data)

AB – AE = AC – AD (Axiom 3)

BE = DC

In Δ BCD and Δ CBE

∠BCD = ∠EBC

BE = DC (Proved)

BC = BC (Common side)

∴ Δ BCD= Δ CBE [SAS postulate]

Question 4.

In the adjoining figure the sides BA and CA have been produced such that BA = AD and CA = AE prove that DE || BC (hint : use the concept of alternate angles.)

Answer:

Δ AED and Δ ABC

AE = AC (data)

AD = AB (data)

∠EAD = ∠BAC

[Vertically opposite angles]

∴ Δ AED = ABC

[SAS postulate]

∴ ∠AED = ∠ACB [Congruent triangle property]

But these are alternate angles.

∴ DE || BC

Consequences of SAS postulate.