Question

In triangle PQR, seg XY is parallel to side QR, M and N are midpoints of seg PY and Seg PR respectively

Answer 1

Answer:

Given: In triangle PQR, XY || QR ,M and N are midpoints of PY and PR .

∴ PM=MY= MN

and PY=YR

∴PY=2PM

and YR=2PM=2MN

Therefore by basic proportionality theorem we have ,

\begin{gathered}\dfrac{PX}{XQ}=\dfrac{PY}{YR}\\\\\Rightarrow\dfrac{PX}{XQ}=\dfrac{2PM}{2MN}\end{gathered}

XQ

PX

=

YR

PY

⇒

XQ

PX

=

2MN

2PM

[]

i) In Δ PXM and Δ PQN, we have

\dfrac{PX}{XQ}=\dfrac{PM}{MN}

XQ

PX

=

MN

PM

\angle{P}=\angle{P}∠P=∠P [ common]

∴ SAS similarity criteria, we have

Δ PXM ≈ Δ PQN

ii) ∵ \dfrac{PX}{XQ}=\dfrac{PM}{MN}

XQ

PX

=

MN

PM

By converse of basic proportionality theorem ,we have

XM || seg QN

Step-by-step explanation:

please mark as brilliant

Answer 2

Answer:

abcdefghijklmnopqrstuvwxyz