Congruence Of Triangles(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

CONGRUENCE OF TRIANGLES MCQs

Total Questions : 103 | Page 11 of 11 pages

(a) In the given figure, show that $Δ A M P ≅ Δ A M Q$ .

(b)

In the given figure, AC = CE and AB $∥$ ED. The value of $x$ is ___ units.
[4 MARKS]

Discuss Question

Answer: Option A. ->
:
Each part: 2 Marks
(a)

In

Δ A M P a n d Δ A M Q

P M = Q M

[Given]

∠ A M P = ∠ A M Q

[Given]

A M = A M

[Common side]

\Rightarrow Δ A M P ≅ Δ A M Q

[SAS congruency criteria]
(b)

In Δ A B C and Δ E D C, A C = C E (given) ∠ B A C = ∠ D E C (since AB||DE and AE is a transversal, so they are alternate angles) ∠ A C B = ∠ E C D (vertically opposite angles) ∴ Δ A B C ≅ Δ E D C (A.S.A. congruence criteria) ∴ A B = D E (sides of congruent triangles) ∴ x + 10 = 2 x - 5 \Rightarrow x - 2 x = - 5 - 10 \Rightarrow - x = - 15 \Rightarrow x = 15 u n i t s

Question 102.

(a) Observe the given triangles and explain, why is $Δ A B C ≅ Δ F E D$ ?

(b) In a $Δ$ ABC, $∠$ B = 50 $^{\circ}$ and $∠$ C is 60 $^{\circ}$ . Find $∠$ A.
[4 MARKS]

Discuss Question

Answer: Option A. ->
:
(a) Proof: 2 Marks

(b) Steps: 1 Mark
Final answer: 1 Mark
(a) In

Δ A B C

and

Δ F E D

∠ B = ∠ E = 90^{\circ}

[Given]

∠ A = ∠ F

[Given]

B C = E D

[Given]

\Rightarrow

Two angles and one side of

Δ A B C

are equal to two angles and one side of

Δ F E D

.
Therefore,

Δ A B C ≅ Δ F E D

[AAS congruence rule]
(b) Sum of the angles of a triangle = 180

^{\circ}

$∠$ A + $∠$ B + $∠$ C = 180 $^{\circ}$

$∠$ A = 180 $^{\circ}$ – (50 $^{\circ}$ + 60 $^{\circ}$ ) = 180 $^{\circ}$ – 110 $^{\circ}$ = 70 $^{\circ}$

Question 103.

In the given figure, $∠ D A B = ∠ C B A$ and AD=BC. Prove that $∠ A C D = ∠ B D C$ . [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Proof: 2 Marks
Steps: 2 Marks

In $Δ A B C a n d Δ B A D$ ,
AD = BC [Given]
$∠ D A B = ∠ C B A$ [Given]
$A B = B A$ [Common]
$∴ Δ A B C ≅ Δ B A D$ (By SAS congruence rule)
$\Rightarrow D B = A C$ [Corresponding parts of corresponding triangles] ...... (1)
In $Δ A D C a n d Δ B C D$
$A D = B C$ [Given]
$D B = A C$ [From (1)]
$D C = C D (C o m m o n)$
$Δ A D C ≅ Δ B C D$ [By SSS congruence rule]
$\Rightarrow ∠ A C D = ∠ B D C$ [Corresponding parts of corresponding triangles]