Question

Please answer this question guys ..... please correct answer

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Answer 1

Given :-

◉ In acute angled△RST. X is a midpoint of RT:

⇒ RX = XT

◉ RN and YT are perpendicular to ST.

To Prove :-

◉ YT = ZR

Solution :-

The solution is simple, we need to find the congruence criteria for △RXZ and △TXY

We are given in the question that RX = XT and ∠RXZ = ∠TXY because these are vertically opposite angles.

But we have only one side and one angle equal in both the triangles. We just need to prove that ZX = XY so we can be sure that these two triangles are congruent to each other.

Now, ST is a straight line and It is also given that, ∠RNS = ∠YTS = 90° , But these are also corresponding angles and two lines are parallel if corresponding angles are equal.

∴ RN || YT

Now, RN || YT and taking RT as transversal, we have

⇒ ∠NRT = ∠YTR (Alternate Interior Angles) ...(1)

So, In △RXZ & △TXY, we have

⇒ RX = XT (given)

⇒ ∠RXZ = ∠TXY (Vertically Opposite Angles)

⇒ ∠NRT = ∠YTR (from [1])

So, By ASA criteria,

△RXZ ⩭△TXY

∴ YT = ZR (C.P.C.T)

Hence, Proved.

Answer 2

Explanation :-

Given :-

• ΔRST is acute angled triangle.

• Point x is a mid point of RT.

• RN and YT are perpendicular to ST.

To Prove :-

• YT = ZR

Proof :-

=> Point x is a mid point of RT.

=> RX = XT --------(1)

=> ∠RXZ = ∠TXY (vertically opposite angels) -------(2)

=> RN || YT & RT is traversal ,

=> ∠NRT = ∠YTR (Alternate interior angle) ------------(3)

=> In ΔRXZ and ΔTXY

=> RX = XT ------( From (1) ]

=> ∠RXZ = ∠TXY ------( From (2) ]

=> ∠NRT = ∠YTR -------(From (3) ]

=> ΔRXZ = ΔTXY --------( From ASA criteria)

=> YT = ZR -----(C.S.C.T)

Hence Proved !!