CTET 2 Math and Science 21 Jan 2024 Paper

Question : 52 of 150

Marks: +1, -0

In triangles ABC and DEF; ∠B = 90°, BC = 8 cm, ∠A = 40°, DE = 8 cm, ∠F = 40° and ∠E = 90°. Then, which of the following statements is true?

Δ ABC ≅ Δ FED, by AAS
Δ ABC ≅ Δ DEF, by RHS
Δ ABC ≅ Δ FED, by RHS
Δ ABC ≅ Δ DFE, by AAS

Validate

Solution:

The angle-angle-side (AAS) theorem is used to determine when two triangles are congruent.
By the theorem, two triangles are congruent if they have two angles of equal measure and one side adjacent to only one of the angles that are equal in length.
Explanation:

△ A B C

△ D E F

\;∠ F=∠ A (40^{∘})

\;∠ B=∠ E (90^{∘})

\;BC=DE(\;\text " Equal in Length "\;)

\; ∴ ∠ ABC ≅ ∠ FED \;\text " (by Angle - Angle - Side Property) "\;

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