Question

In triangle RST , RS = 5CM, angle SRT= 450 & angle RST = 450, Which criterion can be used to construct triangle RST ? *

• A-A-A
• A-S-A
• S-S-S
• NONE OF THESE​

Answer 1

(Correction: The correct value of ∠SRT and ∠RST is45° each)

We have,

RS = 5 cm

∠SRT = ∠RST = 45°

∵ ∠SRT and ∠RST have the same angles

Then, ∠RTS = 180° - (∠SRT + ∠RST)° = 180° (45° + 45°) = 180° - 90° = 90°

∴ ΔRST is a right-angled Δ

Since we have the measurement of the hypotenuse (RS = 5 cm) as well as the angles placed on RS (∠SRT = ∠RST = 45°), we can use the A-S-A or the Angle-Side-Angle criterion of construction to create ΔRST.

Ans) (b) A-S-A

Answer 2

Given :- In triangle RST , RS = 5CM, angle SRT= 45° & angle RST = 45°, Which criterion can be used to construct triangle RST ?

A) A-A-A

B) A-S-A

C) S-S-S

D) NONE OF THESE

Solution :-

in ∆RTS , we have,

→ ∠SRT = 45°

→ ∠RST = 45°

So, by angle sum Property of a ∆,

→ ∠SRT + ∠RST + ∠RTS = 180°

→ 45° + 45° + ∠RTS = 180°

→ 90° + ∠RTS = 180°

→ ∠RTS = 180° - 90°

→ ∠RTS = 90° .

Conclusion :-

• ∆RTS is a right angled ∆ , right angle at T .
• So, Opposite side to right angle is Hypotenuse .=> RS = 5 cm.
• and, also, angle of both ends of hypotenuse are given as 45° .
• we have, two angles equal to 45° and included side, hypotenuse as 5cm.

Therefore, we can conclude that, Angle - Side - Angle , criterion can be used to construct ∆RST .

Hence, Option (B) is correct answer.

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