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Anastaziya [24]
3 years ago
15

In right triangle A EFG m2 E= 25°. In right triangle A HJK, MZ H=25º. Which

Mathematics
1 answer:
maks197457 [2]3 years ago
6 0

Answer:

Therefore the triangles are congruent by Angle Angle similarity postulate.

ΔEFG  ~ ΔHJK ...{ By Angle-Angle similarity postulate}

Step-by-step explanation:

Given:

In right triangle ΔEFG

m∠E= 25°.

In right triangle ΔHJK,

m∠H=25º

To Prove:

ΔEFG  ~ ΔHJK

Proof:

In right triangle ΔEFG  and ΔHJK

m∠ E ≅ m∠ H .......{measure of each angle is 25° given}

m∠ F ≅ m∠ J .........{Both triangle is Right angle Triangle therefore measure angle is 90° each}

∴ ΔEFG  ~ ΔHJK ...{ By Angle-Angle similarity postulate}

Therefore the triangles are congruent by Angle Angle similarity postulate.

ΔEFG  ~ ΔHJK ...{ By Angle-Angle similarity postulate}

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Answer:

Scale factor = 7

Step-by-step explanation:

Dilation with scale factor to map HEFG to DABC will be,

Scale factor = \frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}

                    = \frac{\text{Length of CD}}{\text{Length of GH}}

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                       = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

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Length of GH = Distance between G(0, -1) and H(-1, 0)

                       = \sqrt{(-1-0)^2+(0+1)^2}

                       = \sqrt{2}

Scale factor = \frac{7\sqrt{2} }{\sqrt{2} }

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