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VLD [36.1K]
2 years ago
5

Point A is the point of concurrency of the angle bisectors of ΔDEF.

Mathematics
1 answer:
amm18122 years ago
4 0

The correct answer is option A which is ZA = 3 cm

<h3>What is the triangle?</h3>

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The triangle is shown below.

From the triangle, A is the concurrency point of angle bisectors of all vertices.

Consider ΔAYD,

Using the Pythagorean theorem,

AD² = AY² + YD²

5² = AY² + 4²

25 = AY² + 16

AY² = 25 - 16

AY² = 9

AY = √9 = 3 cm

Consider triangles ADY and ADZ.

∠AYD ≅∠AZD=90

∠ADY≅∠ADZ ( Angle bisector)

AD ≡ AD (common side)

The two triangles are congruent by the AAS postulate.

Therefore, by CPCTE, AY=ZA=3 cm

To know more about triangles follow

brainly.com/question/17335144

#SPJ1

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