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Type: Multiple-Choice
Category: Trigonometry
Level: Grade 11
Standards: HSF-TF.C.8
Author: nsharp1
Created: 4 years ago

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Trigonometry Question

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For the following proof of the Pythagorean Identity, determine the missing statements and reasons in the questions below.

Let triangle ABC be the right triangle pictured below, where

$theta = m ang BAC$ and

$phi = m ang ABC$ . Let

$a$ represent the leg opposite

$ang BAC$ ,

$b$ represent the leg opposite

$ang ABC$ , and

$c$ represent the hypotenuse.

Right Triangle ABC v3

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. Delta ABC " is a right triangle" \ \ \ \ \ \ \ \ \ \ \$	$1. "Given"$
$2. a^2 + b^2 = c^2$	$2. ""$
$3. 1/c^2 (a^2 + b^2) = 1$	$3. "Multiplication Property of Equality"$
$4. a^2/c^2 + b^2/c^2 = 1$	$4. "Distributive Property"$
$5. (a/c)^2 + (b/c)^2 = 1$	$5. "Power of a Quotient Rule"$
$6.$	$6. "Definition of Sine in a right triangle"$
$7.$	$7. "Definition of Cosine in a right triangle"$
$8. sin^2 theta + cos^2 theta = 1$	$8. ""$

Grade 11 Trigonometry CCSS: HSF-TF.C.8

What is the missing reason in step 2?

Given
Pythagorean Theorem
Law of Sines
Summation Property of Addition