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montoyaricardo3550
26.03.2021 •
Mathematics
I need help in the answer it’s math
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Ответ:
E
Step-by-step explanation:
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Ответ:
y = w and Δ ABC ≈ Δ CDE ⇒ answer (a)
Step-by-step explanation:
* Lets explain how to solve the problem
- Δ ABC is a right triangle
∵ m∠B = 90°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠B + z° + y° = 180°
∴ 90° + z° + y° = 180° ⇒ subtract 90° from both sides
∴ z° + y° = 90°
- sinФ = opposite/hypotenuse and cosФ = adjacent/hypotenuse
∵ sin y° = BC/AC
∵ cos z° = BC/AC
∴ sin y° = cos z°
∴ There is a fact in the right triangle if sinФ = cos∝, then Ф + ∝ = 90°
- Lets use this fact to find the answer
∵ sin y° = cos x°
∴ y° + x° = 90°
∵ y° + z° = 90°
∴ x° = z°
- Δ CDE is a right triangle
∵ m∠D = 90
∵ m∠D + x° + w° = 180°
∴ 90° + x° + w° = 180° ⇒ subtract 90° from both sides
∴ x° + w° = 90°
∵ z° + y° = 90°
∵ x° = z°
∴ y° = w°
- In Δ ABC and Δ CDE
∵ y° = w°
∵ x° = z°
∵ m∠B = m∠D
∴ Δ ABC ≈ Δ CDE
* The answer is y = w and Δ ABC ≈ Δ CDE