Question

B. In ∆ABC and ∆RPQ, AB = 4.5 cm, BC = 5 cm, CA = 6√2 cm, PR = 12√2 cm, PQ = 10 cm, QR = 9 cm. If = angle A=75°and angle B =55°,then angle P is equal to (a)75° (b) 55 (c) 50° (d) 130​

Answer 1

Answer:

(C) 50°

Explanation:

1. Prove both triangles similar by ratio of their corresponding sides

2. Find angle C (50°)

3. show angle C = angle P by correspondence

4. Show angle P = 50°

Answer 2

Congruency in triangle

Given:

2 triangles are given .

In ΔABC, AB = 4.5 cm, BC = 5 cm, CA = 6√2 cm, ∠A=75°, ∠B=55°

In ΔRPQ, PR = 12√2 cm, PQ = 10 cm, QR = 9 cm

To Find:

measure of angle P

Step by Step:

Similarity in triangle will help in solving  these type of problem.

Proving the ratio is same for corresponding sides will help in getting desired angles.

In ΔABC,

∠A + ∠B + ∠C = 180°

(sum of all the angles of triangle is 180°)

75° + 55° +  ∠C = 180°

∠C = 180°-130°

∠C= 50°

So,

In ΔABC and ΔRPQ

We can check the ratio of sides given in both triangle,

$\frac{AB}{QR}=\frac{BC}{PQ} =\frac{CA}{PR} = \frac{1}{2}$

So, ΔABC ∼ ΔRPQ

Hence,

∠A = ∠R

∠B = ∠Q

∠C = ∠P

So, ∠P= 50° ( Each pair of corresponding angles are equal.)

Note: The ratio of all the corresponding sides in similar triangles is consistent. All corresponding angles are equal.

Two triangle are said to be congruent if they have same size and same shape, such that they overlap each other.

Two triangles are said to be similar if they have similar shape but not similarly similar size.  

So, Every congruent triangle is also similar but vice versa is not always true.