In Fig. 6.26, AB = AD and ∠BAC = ∠ DAC. Then
(i) ∆___ ≅ ∆ ABC.
(ii) BC = ___.
(iii) ∠BCA = ______.
(iv) Line segment AC bisects _____ and ______.

Solution:

Given, AB = AD

∠BAC = ∠ DAC

We have to fill in the blanks to make the statement true.

Considering triangles ABC and ADC,

Given, AB = AD

Given, ∠BAC = ∠ DAC

Common side = AC

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, ∆ADC ≅ ∆ ABC

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

By CPCT,

The corresponding sides BC and DC are equal.

So, BC = DC

By CPCT,

The corresponding angles BCA and DCA are equal.

So, ∠BAC = ∠ DCA

We observe that the line segment AC bisects ∠A = ∠D

So, ∠BAC = ∠DAC

Similarly, ∠ACD = ∠ACB

✦ Try This: In Fig, ∆ABC ≅ ∆ _____. Fill in the blanks to make the statement true.

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

---

NCERT Exemplar Class 7 Maths Chapter 6 Problem 68

In Fig. 6.26, AB = AD and ∠BAC = ∠ DAC. Then (i) ∆___ ≅ ∆ ABC. (ii) BC = ___. (iii) ∠BCA = ______. (iv) Line segment AC bisects _____ and ______.

Summary:

In Fig. 6.26, AB = AD and ∠BAC = ∠ DAC. Then (i) ∆ADC ≅ ∆ ABC, (ii) BC = DC, (iii) ∠BCA = ∠DCA, (iv) Line segment AC bisects ∠BAD and ∠BCD.

---

☛ Related Questions:

• In Fig. 6.27, (i) ∠TPQ = ∠ _____ + ∠ _____ (ii) ∠UQR = ∠ _____ + ∠ _____ (iii) ∠PRS = ∠ _____ + ∠ _ . . . .
• In a triangle, the sum of squares of two sides is equal to the square of the third side. State wheth . . . .
• Sum of two sides of a triangle is greater than or equal to the third side. State whether the stateme . . . .