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Question Group Info

This question group is public and is used in 4 tests.

Author: nsharp1
No. Questions: 10
Created: Dec 24, 2020
Last Modified: 4 years ago

Proof of Pythagorean Theorem (Sim Triangles)

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Choose the correct missing statements and reasons in the questions below for the following proof.

Given right triangle

$Delta ABC$ , as seen below, with altitude

$bar{CD}$ , prove that

$AC^2 + BC^2 = AB^2$ .

Right Triangle ABCD

Right Triangle ABCD

$\ \ \ \ \ \ \ \ \ \ \ \ \mathbf{"Statement"} \ \ \ \ \ \ \ \ \ \ \ \$	$\mathbf{"Reason"}$
$1. Delta ABC " is a right triangle"$	$1. "Given"$
$2. m ang A + m ang B = 90°$	$2. "Sum of acute angles in right triangle is 90°"$
$3. m ang A = 90° - m ang B$	$3. "Subtraction Property of Equality"$
$4. bar{CD} " is an altitude of " Delta ABC$	$4. "Given"$
$5. ang ADC " is a right angle"$	$5. "Definition of an altitude"$
$6. Delta ADC " is a right triangle"$	$6. ""$
$7. m ang A + m ang ACD = 90°$	$7. ""$
$8. m ang A = 90° - m ang ACD$	$8. "Subtraction Property of Equality"$
$9. 90° - m ang B = 90° - m ang ACD$	$9. ""$
$10. -m ang B = -m ang ACD$	$10. "Subtraction Property of Equality"$
$11. m ang B = m ang ACD$	$11. "Multiplication Property of Equality"$
$12. ang B ~= ang ACD$	$12. "Definition of congruent angles"$
$13. ang A ~= ang A$	$13. "Reflexive Property of Congruence"$
$14.$	$14. "AA Similarity Theorem"$
$15. bar{CD} " is an altitude of " Delta ABC$	$15. "Earlier result"$
$16. ang BDC " is a right angle"$	$16. "Definition of an altitude"$
$17. Delta BDC " is a right triangle"$	$17. "Definition of a right triangle"$
$18. m ang B + m ang BCD = 90°$	$18. ""$
$19. m ang B = 90° - m ang BCD$	$19. "Subtraction Property of Equality"$
$20. m ang A + m ang B = 90°$	$20. "Earlier result"$
$21.m ang B = 90° - m ang A$	$21. "Subtraction Property of Equality"$
$22. 90° - m ang BCD = 90° - m ang A$	$22. "Transitive Property of Equality"$
$23. - m ang BCD = - m ang A$	$23. "Subtraction Property of Equality"$
$24. m ang BCD = m ang A$	$24. "Multiplication Property of Equality"$
$25. ang BCD ~= ang A$	$25. "Definition of congruent angles"$
$26. ang B ~= ang B$	$26. "Reflexive Property of Congruence"$
$27.$	$27. "AA Similarity Theorem"$
$28.$	$28. "Ratios of corr. sides of sim. triangles equal"$
$29. BC^2 = AB * BD$	$29. "Multiplication Property of Equality"$
$30.$	$30. "Ratios of corr. sides of sim. triangles equal"$
$31. AC^2 = AB * AD$	$31. "Multiplication Property of Equality"$
$32. AB = AD+BD$	$32. ""$
$33. AB - BD = AD$	$33. "Subtraction Property of Equality"$
$34. AC^2 + BC^2 = ABAD + ABBD$	$34. ""$
$35. AC^2 + BC^2 = AB(AB - BD) + ABBD$	$35. "Substitution Property of Equality"$
$36. AC^2 + BC^2 = AB^2 - ABBD + ABBD$	$36. "Distribution Property of Equality"$
$37. AC^2 + BC^2 = AB^2$	$37. "Algebra (subtraction)"$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

A.

What is the missing reason in step 6?

Definition of a right triangle
Pythagorean Identity
Sum of angles in a triangle equals 180°
Given

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

B.

What is the missing reason in step 7?

Given
Angle Addition Postulate
Consecutive Interior Angles Theorem
Sum of the acute angles in a right triangle is 90°

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

C.

What is the missing reason in step 9?

Addition Property of Equality
Transitive Property of Equality
Subtraction Property of Equality
Corresponding angles of congruent triangles are congruent

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

D.

What is the missing statement in step 14?

$Delta ACD \ ~ \ Delta CAB$
$Delta ACD \ ~ \ Delta BCA$
$Delta ACD \ ~ \ Delta ABC$
$Delta ACD \ ~ \ Delta ACB$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

E.

What is the missing reason in step 18?

Given
Angle Addition Postulate
Consecutive Interior Angles Postulate
Sum of the acute angles in a right triangle is 90°

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

F.

What is the missing statement in step 27?

$Delta ABC \ ~ \ Delta CBD$
$Delta ABC \ ~ \ Delta CDB$
$Delta ABC \ ~ \ Delta DBC$
$Delta ABC \ ~ \ Delta DCB$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

G.

What is the missing statement in step 28?

$(BC)/(BD) = (BC)/(AB)$
$(BC)/(BD) = (AB)/(BC)$
$(CD)/(AC) = (AB)/(BC)$
$(AB)/(CD) = (AB)/(BC)$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

H.

What is the missing statement in step 30?

$(CD)/(AB) = (AB)/(AC)$
$(BC)/(AD) = (AB)/(AC)$
$(AC)/(AD) = (AC)/(AB)$
$(AC)/(AD) = (AB)/(AC)$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

I.

What is the missing reason in step 32?

Segment Addition Postulate
Given
Midpoint of a line segment
Perpendicular Bisector Theorem

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

J.

What is the missing reason in step 34?

Binomial Expansion Theorem
Addition Property of Equality
Pythagorean Theorem
Perimeter of a triangle