Question

in angle ABC and PQR ,if seg AB=seg PQ,segBCIS non-congruent to angle PQR by which test?

Answer 1

Segment :- ABC is the answer of your question

Answer 2

answer:

ANSWER:

Given : seg PS ≅ seg PT … (1)

seg SQ ≅ seg TR … (2)

In △PST,

seg PS ≅ seg PT

⇒∠S = ∠T … (isosceles triangle theorem)

In △PST, by angle-sum property,

∠P +∠S + ∠T = 180°

⇒ ∠P = 180°- ∠S - ∠T … (3)

Adding (1) and (2), we get:

seg PS +seg SQ ≅seg PT + seg TR

⇒ seg PQ ≅ seg PR

Now, in △PQR,

⇒∠Q = ∠R … (isosceles triangle theorem)

In △PQR, by angle-sum property,

∠P +∠Q + ∠R = 180°

⇒∠P = 180° -∠Q - ∠R … (4)

From (3) and (4),

180° - ∠Q - ∠R = 180° - ∠S -∠T

⇒ ∠Q + ∠R = ∠S + ∠T

But ∠Q = ∠R and ∠S = ∠T

⇒ 2 ∠Q = 2 ∠S

⇒∠Q = ∠S

⇒∠Q = ∠S and ∠T = ∠R

But these angles are corresponding angles formed by transversals PQ and PR, respectively.

So side ST is parallel to side QR.