Congruence and Similarity (Class-7, Experience- 6)

[Exercise- page 140]

E.6.1 In the figure, ABC is an isosceles triangle where AB=AC. What is the measure of the angle marked as ∠A?

Solution:

Given, 

ABC is an isosceles triangle where AB = AC, 

and ∠ACB = 50 degrees. 

Here, ∠ABC must be equal to ∠BAC, as angles opposite equal sides in an isosceles triangle are equal. So, ∠ABC = ∠BAC

Now, to find the measure of angle ∠BAC, we know that the sum of the angles in a triangle is 180 degrees. 

Therefore,

or, ∠BAC + ∠ABC + ∠ACB = 180° 

or, ∠BAC + ∠ABC + 50° = 180°  [known values]

or, ∠BAC + ∠BAC = 180° - 50°  [here, ∠ABC = ∠BAC]

or, 2 * ∠BAC = 130° 

or, ∠BAC = 130  2 degree

∴ ∠BAC = 65°

So, the measure of angle ∠A is 65 degrees. (Answer)

E.6.2 In the figure, ABC is an isosceles triangle where AB=AC. What is the measure of the angle marked as ∠y?

Solution:

Given, 

ABC is an isosceles triangle where AB = AC, 

and ∠BAC = 100 degrees, 

Here, ∠ABC must be equal to ∠ACB, as angles opposite equal sides in an isosceles triangle are equal. So, ∠ABC = ∠ACB

Now, to find the measure of angle ∠ABC, we know that the sum of the angles in a triangle is 180 degrees. 

Therefore,

or, ∠ABC + ∠ACB + ∠BAC = 180° 

or, ∠ABC + ∠ABC + 100° = 180°  [known values]

or, 2 * ∠ABC = 180° - 100°

or, ∠ABC = 80 2 degree

∴ ∠ABC = 40°

So, the measure of angle ∠ABC = y = 40 degrees. (Answer)

E.6.3 Construct a triangle LMN where LM = 2 cm, MN = 3 cm and LN = 2.5 cm. Construct another triangle XYZ where XY = 6 cm, YZ= 9 cm and XZ = 7.5 cm.

Solution:

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E.6.4 In the figure AB and DE are parallel to each other. Answer the following questions using this information. 

(a) What is the value of angle ADE? 

(b) There are two similar triangles in the figure. Find out who they are. Why are they similar? 

(c) Using the properties of similar triangles, find out the length of DE.

Solution:

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