Question

in figure 8.24 triangle pqr is isosceles with PQ equal to PR LM is parallel to QR with L on PQ and M on PR give reason for each of the following statement first angle Q is equal to angle R second angle PLM is equal to angle Q third angle pml is equal to angle R fourth angle PLM is equal to angle pml V triangle PLM is isosceles​

Answer 1

Answer:

Given data:

ΔPQR is isosceles with PQ = PR

LM // QR with L on PQ and M on PR

To prove:

(i)∠Q = ∠R

(ii)∠PLM = ∠Q

(iii)∠PML = ∠R

(iv) ∠PLM = ∠PML

(v)Δ PLM is isosceles

Case 1:

In isosceles ∆ PQR,

Since PQ = PR and we know that the angles opposite to equal sides of triangle is equal .

∴ ∠Q = ∠R …… (i)

Case 2:

Since LM // QR and it is cut by two sides PQ and PR of the triangle.

So, if two parallel are cut by a transversal then the pair of corresponding angles are congruent.

∴ ∠PLM = ∠Q …… (ii)

And,

∠PML = ∠R …… (iii)

Case 3:

From (i), (ii) & (iii), we can say

∠PLM = ∠PML ….. (iv)

Case 4:

From (iv), we get

PL = PM ……. [∵ sides opposite to equal angles are equal]

∴ ∆ PLM is isosceles triangle ….. [∵ PLM is a triangle which has two of its sides PL and PM of equal length]

Answer 2

Answer:

1. PQ=QR
2. corresponding angles
3. corresponding angles
4. from
5. from

Step-by-step explanation:

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