In Fig. 6.18, M is the mid-point of both AC and BD. Then
(a) ∠1 = ∠2
(b) ∠1 = ∠4
(c) ∠2 = ∠4
(d) ∠1 = ∠3

Solution:

Given, M is the mid-point of both AC and BD.

We have to find the correct option.

Since M is the midpoint

AM = CM

BM = DM

Considering triangles AMB and DMC,

We know that the vertically opposite angles are equal.

∠AMB = ∠DMC

The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.

By SAS rule, ΔAMB ≅ ΔCMD

Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.

The corresponding angles are ∠1 and ∠4

Therefore, ∠1 = ∠4

✦ Try This: The hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent. Find the type of congruence criteria?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 43

In Fig. 6.18, M is the mid-point of both AC and BD. Then: (a) ∠1 = ∠2, (b) ∠1 = ∠4, (c) ∠2 = ∠4, (d) ∠1 = ∠3

Summary:

In Fig. 6.18, M is the mid-point of both AC and BD. Then ∠1 = ∠4.

☛ Related Questions:

• If D is the midpoint of the side BC in ∆ABC where AB = AC, then ∠ADC is: (a) 60°, (b) 45°, (c) 120°, . . . .
• Two triangles are congruent, if two angles and the side included between them in one of the triangle . . . .
• By which congruence criterion, the two triangles in Fig. 6.19 are congruent? (a) RHS, (b) ASA, (c) S . . . .