# RD Sharma Solutions For Class 7 Maths Chapter 16 Congruence Exercise 16.5

RD Sharma Solutions for Class 7 Maths Exercise 16.5 Chapter 16 Congruence are available here. The expert faculty at BYJUâ€™S have formulated solutions based on the marks allotted for each step of a problem. The main objective is to help students in solving problems, in turn, which makes the subject easier to understand. Our experts have provided chapter-wise solutions which help students perform well in the exam. Students can download the RD Sharma Solutions for Class 7 for further reference. This exercise explains RHS congruence condition for two congruent triangles.

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Exercise 16.5 Page No: 16.23

1. In each of the following pairs of right triangles, the measures of some parts are indicated alongside. State by the application of RHS congruence condition which are congruent, and also state each result in symbolic form. (Fig. 46)

Solution:

(i) âˆ ADB = âˆ BCA = 90o

AD = BC and hypotenuse AB = hypotenuse AB

Therefore, by RHS Î”ADB â‰… Î”ACB

Hypotenuse AC = hypotenuse AB (Given)

âˆ ADB + 90o = 180o

âˆ ADB = 180o â€“ 90o = 90o

(iii) Hypotenuse AO = hypotenuse DO

BO = CO

âˆ B = âˆ C = 90o

Therefore, by RHS, Î”AOBâ‰…Î”DOC

(iv) Hypotenuse AC = Hypotenuse CA

BC = DC

âˆ ABC = âˆ ADC = 90o

Therefore, by RHS, Î”ABC â‰… Î”ADC

(v) BD = DB

Hypotenuse AB = Hypotenuse BC, as per the given figure,

âˆ BDA + âˆ BDC = 180o

âˆ BDA + 90o = 180o

âˆ BDA= 180o â€“ 90o = 90o

âˆ BDA = âˆ BDC = 90o

Therefore, by RHS, Î”ABD â‰… Î”CBD

2. Î” ABC is isosceles with AB = AC. AD is the altitude from A on BC.

(i) Is Î”ABD â‰… Î”ACD?

(ii) State the pairs of matching parts you have used to answer (i).

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

Solution:

(i) Yes, Î”ABD â‰… Î”ACD by RHS congruence condition.

(ii) We have used Hypotenuse AB = Hypotenuse AC

(iii)Yes, it is true to say that BD = DC (corresponding parts of congruent triangles)

Since we have already proved that the two triangles are congruent.

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3. Î”ABC is isosceles with AB = AC. Also. AD âŠ¥ BC meeting BC in D. Are the two triangles ABD and ACD congruent? State in symbolic form. Which congruence condition do you use? Which side of ADC equals BD? Which angle of Î” ADC equals âˆ B?

Solution:

We have AB = AC â€¦â€¦ (i)

AD = DA (common) â€¦â€¦ (ii)

Therefore, from (i), (ii) and (iii), by RHS congruence condition, Î”ABD â‰… Î”ACD, the triangles are congruent.

Therefore, BD = CD.

And âˆ ABD = âˆ ACD (corresponding parts of congruent triangles)

4. Draw a right triangle ABC. Use RHS condition to construct another triangle congruent to it.

Solution:

Consider

Î” ABC with âˆ B as right angle.

We now construct another triangle on base BC, such that âˆ C is a right angle and AB = DC

Also, BC = CB

Therefore by RHS, Î”ABC â‰… Î”DCB

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5.In fig. 47, BD and CE are altitudes of Î” ABC and BD = CE.

(i) Is Î”BCD â‰… Î”CBE?

(ii) State the three pairs or matching parts you have used to answer (i)

Solution:

(i) Yes, Î”BCD â‰… Î”CBE by RHS congruence condition.

(ii) We have used hypotenuse BC = hypotenuse CB

BD = CE (Given in question)

And âˆ BDC = âˆ CEB = 90o