The study materials of RD Sharma Solutions for Class 7 Maths Exercise 16.3 of Chapter 16, in the form of PDF, is available here. Students who want to score high in Maths can download these materials from the given links. Our expert team have formulated RD Sharma Solutions for Class 7 to help and fulfill the dreams of students. This exercise has thirty questions based on SAS congruence condition along with proof.

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Exercise 16.3 Page No: 16.14

**1. By applying SAS congruence condition, state which of the following pairs (Fig. 28) of triangle are congruent. State the result in symbolic form**

**Solution:**

(i) From the figure we have OA = OC and OB = OD and

âˆ AOB =Â âˆ COD which are vertically opposite angles.

Therefore by SAS condition, Î”AOB â‰…Î”COD

(ii) From the figure we have BD = DC

âˆ ADB =Â âˆ ADC = 90^{o} and AD = DA

Therefore, by SAS condition, Î”ADB â‰…Î”ADC.

(iii) From the figure we have AB = DC

âˆ ABD =Â âˆ CDB and BD = DB

Therefore, by SAS condition, Î”ABD â‰…Î”CBD

(iv) We have BC = QR

ABC = PQR = 90^{o}

And AB = PQ

Therefore, by SAS condition,Â Î”ABCâ‰…Â Î”PQR.

**2. State the condition by which the following pairs of triangles are congruent.**

**Solution: **

(i) AB = AD

BC = CD and AC = CA

Therefore by SSS condition, Î”ABCâ‰… Î”ADC

(ii) AC = BD

AD = BC and AB = BA

Therefore, by SSS condition, Î”ABD â‰… Î”BAC

(iii) AB = AD

âˆ BAC =Â âˆ DAC and AC = CA

Therefore by SAS condition, Î”BAC â‰… Î”DAC

(iv) AD = BC

âˆ DAC =Â âˆ BCA and AC = CA

Therefore, by SAS condition, Î”ABC â‰… Î”ADC

**3.** **In fig. 30, line segments AB and CD bisect each other at O. Which of the following statements is true?**

**(i)Â Î”AOC â‰… Î”DOB**

**(ii)Â Î”AOC â‰… Î”BOD**

**(iii)Â Î”AOC â‰… Î”ODB**

**State the three pairs of matching parts, you have used to arrive at the answer.**

**Solution:**

From the figure we have,

AO = OB

And, CO = OD

Also, AOC = BOD

Therefore, by SAS condition,Â Î”AOC â‰… Î”BOD

Hence, (ii) statement is true.

**4. Line-segments AB and CD bisect each other at O. AC and BD are joined forming triangles AOC and BOD. State the three equality relations between the parts of the two triangles that are given or otherwise known. Are the two triangles congruent? State in symbolic form, which congruence condition do you use?**

**Solution:**

We have AO = OB and CO = OD

Since AB and CD bisect each other at 0.

AlsoÂ âˆ AOC =Â âˆ BOD

Since they are opposite angles on the same vertex.

Therefore by SAS congruence condition, Î”AOC â‰… Î”BOD

**5. Î”ABC is isosceles with AB = AC. Line segment AD bisectsÂ **âˆ **A and meets the base BC in D.**

**(i) Is Î”ADB â‰… Î”ADC?**

**(ii) State the three pairs of matching parts used to answer (i).**

**(iii) Is it true to say that BD = DC?**

**Solution:**

(i) We have AB = AC (Given)

âˆ BAD =Â âˆ CAD (AD bisectsÂ âˆ BAC)

Therefore by SAS condition of congruence, Î”ADB â‰… Î”ADC

(ii) We have used AB, AC;Â âˆ BAD =Â âˆ CAD; AD, DA.

(iii) Now, Î”ADBâ‰…Î”ADC

Therefore by corresponding parts of congruent triangles

BD = DC.

**6. In Fig. 31, AB = AD and âˆ BAC = âˆ DAC.**

**(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.**

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

**(a) âˆ ABC =**

**(b) âˆ ACD =**

**(c) Line segment AC bisects â€¦.. And â€¦â€¦..**

**Solution:**

i) AB = AD (given)

âˆ BAC = âˆ DAC (given)

AC = CA (common)

Therefore by SAS condition of congruency, Î”ABC â‰… Î”ADC

ii) âˆ ABC = âˆ ADC (corresponding parts of congruent triangles)

âˆ ACD = âˆ ACB (corresponding parts of congruent triangles)

Line segment AC bisects âˆ A and âˆ C.

**7. In fig. 32, AB || DC and AB = DC.**

**(i) Is Î”ACD â‰… Î”CAB?**

**(ii) State the three pairs of matching parts used to answer (i).**

**(iii) Which angle is equal to âˆ CAD?**

**(iv) Does it follow from (iii) that AD || BC?**

**Solution:**

(i) Yes by SAS condition of congruency, Î”ACD â‰… Î”CAB.

(ii) We have used AB = DC, AC = CA and âˆ DCA = âˆ BAC.

(iii) âˆ CAD = âˆ ACB since the two triangles are congruent.

(iv) Yes this follows from AD parallel to BC as alternate angles are equal. lf alternate angles are equal then the lines are parallel