(a) Answer It is proved that Δ A B D is congruent to Δ C B D . Explanation Given: ∠ C D B ≅ ∠ A D B D B ¯ ⊥ A C ¯ Calculation: The proof is as follows. Statement Reasons ∠ C D B ≅ ∠ A D B D B ¯ ⊥ A C ¯ Given ∠ A B D and ∠ C B D are right angles Definition of perpendicular lines ∠ A B D ≅ ∠ C B D Right Angles Congruence Theorem B D ¯ ≅ B D ¯ Reflexive Property of Congruence Δ A B D ≅ Δ C B D ASA Congruence Theorem Therefore, it is proved that Δ A B D is congruent to Δ C B D . (b) To determine To verify: That the Δ A C D is isosceles. Answer It is verified that Δ A C D is isosceles. Explanation Given: ∠ C D B ≅ ∠ A D B D B ¯ ⊥ A C ¯ Calculation: Since Δ A B D ≅ Δ C B D and corresponding parts of congruent triangles are congruent. Therefore, A D ¯ ≅ C D ¯ , that is Δ A C D is isosceles. (c) To determine To find: Whether moving away from the mirror have any effect on the amount of his or her reflection person sees. Answer The answer is no. Explanation Given: The Δ A C D is Calculation: The answer is no, because Δ A C D isosceles. The girl sees her toes in the bottom of the mirror. This remains true as she moves backwards because Δ A C D remains isosceles.

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 12.6, Problem 29E

(a)

To determine

To prove: That the $ΔABD$ is congruent to $ΔCBD$ .

(a)

Expert Solution

Answer to Problem 29E

It is proved that $ΔABD$ is congruent to $ΔCBD$ .

Explanation of Solution

Given:

$∠CDB≅∠ADBDB¯⊥AC¯$

Calculation:

The proof is as follows.

Statement	Reasons
$∠CDB≅∠ADBDB¯⊥AC¯$	Given
$∠ABD$ and $∠CBD$ are right angles	Definition of perpendicular lines
$∠ABD≅∠CBD$	Right Angles Congruence Theorem
$BD¯≅BD¯$	Reflexive Property of Congruence
$ΔABD≅ΔCBD$	ASA Congruence Theorem

Therefore, it is proved that $ΔABD$ is congruent to $ΔCBD$ .

(b)

To determine

To verify: That the $ΔACD$ is isosceles.

(b)

Expert Solution

Answer to Problem 29E

It is verified that $ΔACD$ is isosceles.

Explanation of Solution

Given:

$∠CDB≅∠ADBDB¯⊥AC¯$

Calculation:

Since $ΔABD≅ΔCBD$ and corresponding parts of congruent triangles are congruent.

Therefore, $AD¯≅CD¯$ , that is $ΔACD$ is isosceles.

(c)

To determine

To find: Whether moving away from the mirror have any effect on the amount of his or her reflection person sees.

(c)

Expert Solution

Answer to Problem 29E

The answer is no.

Explanation of Solution

Given:

The $ΔACD$ is

Calculation:

The answer is no, because $ΔACD$ isosceles. The girl sees her toes in the bottom of the mirror. This remains true as she moves backwards because $ΔACD$ remains isosceles.

Chapter 12.6, Problem 28E

Chapter 12.6, Problem 30E

Chapter 12 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.1 - Prob. 44E Ch. 12.1 - Prob. 45E Ch. 12.1 - Prob. 46E Ch. 12.1 - Prob. 47E Ch. 12.1 - Prob. 48E Ch. 12.1 - Prob. 49E Ch. 12.1 - Prob. 50E Ch. 12.1 - Prob. 51E Ch. 12.1 - Prob. 52E Ch. 12.1 - Prob. 53E Ch. 12.1 - Prob. 54E Ch. 12.1 - Prob. 55E Ch. 12.1 - Prob. 56E Ch. 12.1 - Prob. 57E Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Prob. 27E Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - Prob. 12E Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - Prob. 19E Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.3 - Prob. 27E Ch. 12.3 - Prob. 28E Ch. 12.3 - Prob. 29E Ch. 12.3 - Prob. 30E Ch. 12.3 - Prob. 31E Ch. 12.3 - Prob. 32E Ch. 12.3 - Prob. 33E Ch. 12.3 - Prob. 34E Ch. 12.3 - Prob. 35E Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - Prob. 6E Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Prob. 16E Ch. 12.4 - Prob. 17E Ch. 12.4 - Prob. 18E Ch. 12.4 - Prob. 19E Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Prob. 24E Ch. 12.4 - Prob. 25E Ch. 12.4 - Prob. 26E Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - Prob. 33E Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.4 - Prob. 38E Ch. 12.4 - Prob. 39E Ch. 12.4 - Prob. 40E Ch. 12.4 - Prob. 41E Ch. 12.4 - Prob. 42E Ch. 12.4 - Prob. 43E Ch. 12.4 - Prob. 44E Ch. 12.4 - Prob. 1Q Ch. 12.4 - Prob. 2Q Ch. 12.4 - Prob. 3Q Ch. 12.4 - Prob. 4Q Ch. 12.4 - Prob. 5Q Ch. 12.4 - Prob. 6Q Ch. 12.4 - Prob. 7Q Ch. 12.4 - Prob. 8Q Ch. 12.4 - Prob. 9Q Ch. 12.4 - Prob. 10Q Ch. 12.4 - Prob. 11Q Ch. 12.4 - Prob. 12Q Ch. 12.4 - Prob. 13Q Ch. 12.4 - Prob. 14Q Ch. 12.4 - Prob. 15Q Ch. 12.4 - Prob. 16Q Ch. 12.5 - Prob. 1E Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - Prob. 4E Ch. 12.5 - Prob. 5E Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - Prob. 9E Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Prob. 20E Ch. 12.5 - Prob. 21E Ch. 12.5 - Prob. 22E Ch. 12.5 - Prob. 23E Ch. 12.5 - Prob. 24E Ch. 12.5 - Prob. 25E Ch. 12.5 - Prob. 26E Ch. 12.5 - Prob. 27E Ch. 12.5 - Prob. 28E Ch. 12.5 - Prob. 29E Ch. 12.5 - Prob. 30E Ch. 12.5 - Prob. 31E Ch. 12.5 - Prob. 32E Ch. 12.5 - Prob. 33E Ch. 12.5 - Prob. 34E Ch. 12.5 - Prob. 35E Ch. 12.5 - Prob. 36E Ch. 12.5 - Prob. 37E Ch. 12.5 - Prob. 38E Ch. 12.5 - Prob. 39E Ch. 12.5 - Prob. 40E Ch. 12.6 - Prob. 1E Ch. 12.6 - Prob. 2E Ch. 12.6 - Prob. 3E Ch. 12.6 - Prob. 4E Ch. 12.6 - Prob. 5E Ch. 12.6 - Prob. 6E Ch. 12.6 - Prob. 7E Ch. 12.6 - Prob. 8E Ch. 12.6 - Prob. 9E Ch. 12.6 - Prob. 10E Ch. 12.6 - Prob. 11E Ch. 12.6 - Prob. 12E Ch. 12.6 - Prob. 13E Ch. 12.6 - Prob. 14E Ch. 12.6 - Prob. 15E Ch. 12.6 - Prob. 16E Ch. 12.6 - Prob. 17E Ch. 12.6 - Prob. 18E Ch. 12.6 - Prob. 19E Ch. 12.6 - Prob. 20E Ch. 12.6 - Prob. 21E Ch. 12.6 - Prob. 22E Ch. 12.6 - Prob. 23E Ch. 12.6 - Prob. 24E Ch. 12.6 - Prob. 25E Ch. 12.6 - Prob. 26E Ch. 12.6 - Prob. 27E Ch. 12.6 - Prob. 28E Ch. 12.6 - Prob. 29E Ch. 12.6 - Prob. 30E Ch. 12.6 - Prob. 31E Ch. 12.6 - Prob. 32E Ch. 12.6 - Prob. 33E Ch. 12.6 - Prob. 34E Ch. 12.6 - Prob. 35E Ch. 12.6 - Prob. 36E Ch. 12.6 - Prob. 37E Ch. 12.6 - Prob. 38E Ch. 12.7 - Prob. 1E Ch. 12.7 - Prob. 2E Ch. 12.7 - Prob. 3E Ch. 12.7 - Prob. 4E Ch. 12.7 - Prob. 5E Ch. 12.7 - Prob. 6E Ch. 12.7 - Prob. 7E Ch. 12.7 - Prob. 8E Ch. 12.7 - Prob. 9E Ch. 12.7 - Prob. 10E Ch. 12.7 - Prob. 11E Ch. 12.7 - Prob. 12E Ch. 12.7 - Prob. 13E Ch. 12.7 - Prob. 14E Ch. 12.7 - Prob. 15E Ch. 12.7 - Prob. 16E Ch. 12.7 - Prob. 17E Ch. 12.7 - Prob. 18E Ch. 12.7 - Prob. 19E Ch. 12.7 - Prob. 20E Ch. 12.7 - Prob. 21E Ch. 12.7 - Prob. 22E Ch. 12.7 - Prob. 23E Ch. 12.7 - Prob. 24E Ch. 12.7 - Prob. 25E Ch. 12.8 - Prob. 1E Ch. 12.8 - Prob. 2E Ch. 12.8 - Prob. 3E Ch. 12.8 - Prob. 4E Ch. 12.8 - Prob. 5E Ch. 12.8 - Prob. 6E Ch. 12.8 - Prob. 7E Ch. 12.8 - Prob. 8E Ch. 12.8 - Prob. 9E Ch. 12.8 - Prob. 10E Ch. 12.8 - Prob. 11E Ch. 12.8 - Prob. 12E Ch. 12.8 - Prob. 13E Ch. 12.8 - Prob. 14E Ch. 12.8 - Prob. 15E Ch. 12.8 - Prob. 16E Ch. 12.8 - Prob. 17E Ch. 12.8 - Prob. 18E Ch. 12.8 - Prob. 19E Ch. 12.8 - Prob. 20E Ch. 12.8 - Prob. 21E Ch. 12.8 - Prob. 22E Ch. 12.8 - Prob. 23E Ch. 12.8 - Prob. 24E Ch. 12.8 - Prob. 25E Ch. 12.8 - Prob. 26E Ch. 12.8 - Prob. 27E Ch. 12.8 - Prob. 28E Ch. 12.8 - Prob. 29E Ch. 12 - Prob. 1CR Ch. 12 - Prob. 2CR Ch. 12 - Prob. 3CR Ch. 12 - Prob. 4CR Ch. 12 - Prob. 5CR Ch. 12 - Prob. 6CR Ch. 12 - Prob. 7CR Ch. 12 - Prob. 8CR Ch. 12 - Prob. 9CR Ch. 12 - Prob. 10CR Ch. 12 - Prob. 11CR Ch. 12 - Prob. 12CR Ch. 12 - Prob. 13CR Ch. 12 - Prob. 14CR Ch. 12 - Prob. 15CR Ch. 12 - Prob. 16CR Ch. 12 - Prob. 17CR Ch. 12 - Prob. 18CR Ch. 12 - Prob. 19CR Ch. 12 - Prob. 20CR Ch. 12 - Prob. 21CR Ch. 12 - Prob. 22CR Ch. 12 - Prob. 23CR Ch. 12 - Prob. 24CR Ch. 12 - Prob. 25CR Ch. 12 - Prob. 1CT Ch. 12 - Prob. 2CT Ch. 12 - Prob. 3CT Ch. 12 - Prob. 4CT Ch. 12 - Prob. 5CT Ch. 12 - Prob. 6CT Ch. 12 - Prob. 7CT Ch. 12 - Prob. 8CT Ch. 12 - Prob. 9CT Ch. 12 - Prob. 10CT Ch. 12 - Prob. 11CT Ch. 12 - Prob. 1CA Ch. 12 - Prob. 2CA Ch. 12 - Prob. 3CA Ch. 12 - Prob. 4CA Ch. 12 - Prob. 5CA Ch. 12 - Prob. 6CA Ch. 12 - Prob. 7CA Ch. 12 - Prob. 8CA

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