Question

In the given figure it is given that XY=XZ X is the mid-point of QR and exterior angle of /_QXY is equal to exterior angle of /_RXZ.Then prove that PY=PZ.​

Answer 1

Answer:

ln the given fihure it is given that xy=xz x is the

Answer 2

Solution :-

→∠QXZ =∠RXY { given that exterior angle of ∠RXZ and ∠QXY are equal. }

→ ∠QXZ -∠YXZ = ∠RXY - ∠YXZ

→ ∠QXY = ∠RXZ -------- Eqn.(1)

So, in ∆QXY and ∆RXZ we have,

→ QX = RX { given that X is the mid point of QR. }

→ ∠QXY = ∠RXZ { from Eqn.(1) }

→ XY = XZ J { given }

then,

→ ∆QXY ≅ ∆RXZ { By SAS congruence rule . }

therefore,

• ∠YQX = ∠ZRX ------- Eqn.(2)
• YQ = ZR ---------- Eqn.(3)
• When two ∆'s are congruent , their corresponding sides are equal in length and their corresponding angles are equal in measure .

now, from Eqn.(2) ,

→ ∠YQX = ∠ZRX

→ ∠PQR = ∠PRQ

hence,

→ PQ = PR { The sides opposite to equal angles of a ∆ are equal in measure. }

→ PQ - YQ = PR - ZR

using Eqn.(3) ,

→ PY = PZ (Proved.)

" ∴ PY is equal to PZ ."

Learn More :-

in triangle ABC seg DE parallel side BC. If 2 area of triangle ADE = area of quadrilateral DBCE find AB : AD show that B...

https://brainly.in/question/15942930

2) In ∆ABC seg MN || side AC, seg MN divides ∆ABC into two parts of equal area. Determine the value of AM / AB

https://brainly.in/question/37634605