Question

If ∆ PQR and ∆ SUV are equilateral triangles and PQ = SU , then the condition under which ∆ POR = ∆ SUV is –

A) ASA
B) SSS
C) SAS
D) RHS
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Answer 1

Answer:

SSS.

Step-by-step explanation:

Triangle PQR and triangle SUV are both equilateral triangles.

•°• In triangles PQR and SUV,

PQ=SU [Given]

•°• QR=UV [ equilateral triangles ]

•°• RP=VS [ equilateral triangles ]

•°• Tri. PQR = Tri. SUV [ by SSS ]

°•° If PQ=SU and both the triangles are equilateral triangles then the measure of all sides would be equal of both the triangles and if one side of both triangles is equal then all the sides would be equal to each other. Hence, triangle PQR is congruent to triangle SUV.

Answer 2

D) RHS

it is RHS property of the triangle since PORQ is a rectangle and when divided into two it becomes two equal triangles. And another triangle SUV is also an equilateral triangle and triangle PQR= triangle SUV. Since

angle PQ = angle SU (given)

angle PR = angle SV

angle UV = angle QR

therefore triangle PQR = triangle SUV

Also triangle POR = triangle SUV, since

angle PO = angle SU

angle OR = angle UV

angle PR = angle SV

therefore triangle POR = triangle SUV