The DAV Maths Class 7 Solutions and **DAV Class 7 Maths Chapter 9 Worksheet 2** Solutions of Construction of Triangles offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 9 WS 2 Solutions

Question 1.

In ∆ ABC and ∆ DEF, AB = DE and BC = EF (See fig.). What additional information is required to make the two triangles congruent by SAS congruence condition ?

Answer:

In ∆ ABC and ∆ DEF,

AB = DE and BC = EF

included ∠ABC = ∠DEF

Hence, additional condition for congruency required is ∠ABC must be equal to

Question 2.

∆ ABC is isosceles with AB = AC (See fig.).

Line segment AD bisects ∠A and meets the base BC at D. Find the third pair of corresponding parts which make ∆ ADB ≅ ∆ ADC by SAS congruence condition. Is it true to say that BD = CD? Why?

Answer:

In ∆ ABD and ∆ ACD,

AB = AC [given]

AD = AD

And ∠B AD = ∠CAD

∆ABD = ∆ ACD

Hence the third condition required is ∠BAD = ∠CAD.

Question 3.

In the given figure, AB ∥ DC and AB = DC.

(i) Is ∠BAC = ∠DCA? Why?

Answer:

AB ∥ DC and AC is transversal (given)

∴ ∠BAC = ∠ACD (alternate angles)

AB = DC (given)

AC = AC (Common)

(ii) Is ∆ABC ≅ ∆CDA by SAS congruence condition?

Answer:

∴ ∆ABC ≅ ∆CDA (By SAS)

(iii) State the three facts that you have used to answer (ii).

Answer:

(a) AB = DC (given)

(b) AC = AC (Common)

(c) ∠BAC = ∠ACD (Alternate angles)

Question 4.

In the given figure, which pairs of triangles are congruent by SAS congruence condition?

Answer:

In ∆ABC and ∆ DEF,

AB = DE = 3 cm (given)

BC = DF = 4 cm (given)

∠ABC = ∠EDF = 70° (given)

∆ABC ≅ ∆DEF (By SAS)

Answer:

In ∆PQS and ∆RQS,

PS = QR = 4 cm (given)

QS = QS = 5.8 cm (given)

∠P = ∠R = 90° (given)

∆PQS ≅ ∆RQS (By RHS)

Answer:

In ∆PQR and ∆XYZ,

PR = XY = 4 cm (given)

QR = YZ = 2 cm (given)

∠PRQ = ∠X YZ = 55° (given)

∆PQR ≅ ∆XYZ (By SSS)

Answer:

In ∆ABD and ∆ABC,

AD = BC (given)

DB = AC (given)

AB = AB (Common)

∆ABD ≅ ∆ABC (By SAS)

Answer:

In ∆PQS and ∆RQS,

PS = QR = 4 cm (given)

QS = QS = 5.8 cm (given)

∠P = ∠R = 90° (given)

∆PQS ≅ ∆RQS (By RHS)

Answer:

In ∆ABD and ∆ABC,

AD = BC (given)

DB = AC (given)

AB = AB (Common)

∆ABD ≅ ∆ABC (Common)

Question 5.

In the given figure, AB = AD and ∠BAC = ∠DAC

(i) State in symbolic form, the congruence of two triangles ABC and ADC is true. Also, state the congruence condition used.

Answer:

In ∆ABC and ∆ADC,

AB = AD (given)

∠BAC = ∠DAC (given)

AC = AC (Common)

∆ABC ≅ ∆ADC (Common)

(ii) Complete each of the following, so as to make it true.

(a) ∠ABC = ________________

(b) ∠ACD = ________________

(c) Line segment AC bisects ________________ and ________________

Answer:

(a) ∠ABC = ∠ADC

(b) ∠ACD = ∠ACB

(c) ∠BAD and ∠BCD