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Geometry

Harold R. Jacobs

Chapter 8

Transformations - all with Video Answers

Educators

Section 1

Reflections

00:33

Problem 1

$$\begin{aligned}
&\text { In } \triangle \mathrm{BUD} \text { and } \triangle \mathrm{PES}, \angle \mathrm{B}=\angle \mathrm{P}, \frac{\mathrm{BU}}{\mathrm{PE}}=\frac{\mathrm{BD}}{\mathrm{PS}}\\
&\overline{\mathrm{UA}} \perp \overline{\mathrm{BD}}, \text { and } \overline{\mathrm{ET}} \perp \overline{\mathrm{PS}}
\end{aligned}$$
$$\text { Why is } \triangle \mathrm{BUD} \sim \triangle \mathrm{PES} ?$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:27

Problem 2

$$\begin{aligned}
&\text { In } \triangle \mathrm{BUD} \text { and } \triangle \mathrm{PES}, \angle \mathrm{B}=\angle \mathrm{P}, \frac{\mathrm{BU}}{\mathrm{PE}}=\frac{\mathrm{BD}}{\mathrm{PS}}\\
&\overline{\mathrm{UA}} \perp \overline{\mathrm{BD}}, \text { and } \overline{\mathrm{ET}} \perp \overline{\mathrm{PS}}
\end{aligned}$$
$$\text { Why is } \angle \mathrm{D}=\angle \mathrm{S} ?$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:27

Problem 3

$$\begin{aligned}
&\text { In } \triangle \mathrm{BUD} \text { and } \triangle \mathrm{PES}, \angle \mathrm{B}=\angle \mathrm{P}, \frac{\mathrm{BU}}{\mathrm{PE}}=\frac{\mathrm{BD}}{\mathrm{PS}}\\
&\overline{\mathrm{UA}} \perp \overline{\mathrm{BD}}, \text { and } \overline{\mathrm{ET}} \perp \overline{\mathrm{PS}}
\end{aligned}$$
$$\text { Why is } \frac{U A}{E T}=\frac{B D}{P S} ?$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:30

Problem 4

The following exercises are about $\triangle \mathrm{NAP}$ and $\triangle \mathrm{LES}$
Show why $\Varangle \mathrm{A}$ and $\Varangle \mathrm{E}$ are right angles.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:41

Problem 5

The following exercises are about $\triangle \mathrm{NAP}$ and $\triangle \mathrm{LES}$
Are the triangles similar?
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:12

Problem 6

The following exercises are about $\triangle \mathrm{NAP}$ and $\triangle \mathrm{LES}$
Explain why or why not.
(GRAPH CANT COPY)

Heather Zimmers
Heather Zimmers
Numerade Educator
00:19

Problem 7

The following exercises are about $\triangle \mathrm{DUB}$ and $\triangle \mathrm{LIN}$.
Find $\angle \mathrm{U}$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:20

Problem 8

The following exercises are about $\triangle \mathrm{DUB}$ and $\triangle \mathrm{LIN}$.
Are the triangles similar?
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:54

Problem 9

The following exercises are about $\triangle \mathrm{DUB}$ and $\triangle \mathrm{LIN}$.
Explain why or why not.
(GRAPH CANT COPY)

Heather Zimmers
Heather Zimmers
Numerade Educator
00:36

Problem 10

\frac{\text { In } \triangle L B N, \overline{N I}}{N L} \| \overline{O I}
$$\text { Why is } \angle \mathrm{L}=\angle \mathrm{OIB} ?$$
(GRAPH CANT COPY)

Ashley High
Ashley High
Numerade Educator
00:28

Problem 11

$$\text { In } \triangle \mathrm{LBN}, \overline{\mathrm{NI}} \perp \overline{\mathrm{LB}}, \overline{\mathrm{OS}} \perp \overline{\mathrm{LB}}, \text { and }$$
$$\overline{\mathrm{NL}} \| \overline{\mathrm{Ol}}$$
$$\text { Why is } \triangle \mathrm{LBN} \sim \triangle \mathrm{IBO} ?$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:09

Problem 12

$$\text { In } \triangle \mathrm{LBN}, \overline{\mathrm{NI}} \perp \overline{\mathrm{LB}}, \overline{\mathrm{OS}} \perp \overline{\mathrm{LB}}, \text { and }$$
$$\overline{\mathrm{NL}} \| \overline{\mathrm{Ol}}$$
$$\text { Why is } \frac{\mathrm{NI}}{\mathrm{OS}}=\frac{\mathrm{LB}}{\mathrm{IB}} ?$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:36

Problem 13

Solve for $x$ in each of these figures.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:36

Problem 14

Solve for $x$ in each of these figures.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:36

Problem 15

Solve for $x$ in each of these figures.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:36

Problem 16

Solve for $x$ in each of these figures.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:33

Problem 17

In the figure below, $\triangle \mathrm{IST} \sim \triangle \mathrm{NBU}$, $\overline{\mathrm{SA}} \perp \overline{\mathrm{IT}}$ and $\overline{\mathrm{BL}} \perp \overline{\mathrm{NU}} .$ Find each of the following numbers.
BL.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:15

Problem 18

In the figure below, $\triangle \mathrm{IST} \sim \triangle \mathrm{NBU}$, $\overline{\mathrm{SA}} \perp \overline{\mathrm{IT}}$ and $\overline{\mathrm{BL}} \perp \overline{\mathrm{NU}} .$ Find each of the following numbers.
$$\alpha \triangle \mathrm{IST}$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:15

Problem 19

In the figure below, $\triangle \mathrm{IST} \sim \triangle \mathrm{NBU}$, $\overline{\mathrm{SA}} \perp \overline{\mathrm{IT}}$ and $\overline{\mathrm{BL}} \perp \overline{\mathrm{NU}} .$ Find each of the following numbers.
$$\alpha \triangle \mathrm{NBU}$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:29

Problem 20

Find each of the following ratios as a common fraction in lowest terms.
$$\frac{1 S}{N B}$$

Christopher Stanley
Christopher Stanley
Numerade Educator
00:31

Problem 21

Find each of the following ratios as a common fraction in lowest terms.
$$\frac{\alpha \Delta \mathrm{IST}}{\alpha \triangle \mathrm{NBU}}$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:05

Problem 22

Given: $\triangle$ MIA with $\mathrm{MI}=\mathrm{IA}$ and
$$
\mathrm{LN}=\mathrm{NA} ; \angle \mathrm{I}=\angle 1
$$
Prove: $\triangle \mathrm{MIA} \sim \triangle \mathrm{LNA}$ by using
the S.A.S. Similarity Theorem.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:46

Problem 23

Using the information given in Exercise 22, prove $\triangle \mathrm{MIA} \sim \triangle \mathrm{LNA}$ by using the A. A. Similarity Theorem.
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:03

Problem 24

$$\begin{array}{ll}
\text {Given:} & \frac{\mathrm{CA}}{\mathrm{CI}}=\frac{\mathrm{CO}}{\mathrm{CR}} \\
\text { Prove: } & \frac{\mathrm{CI}}{\mathrm{AO}} \| \overline{\mathrm{IR}}
\end{array}$$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:43

Problem 25

Given: $\quad \mathrm{RE}$ is the geometric mean between RO and $\mathrm{RM}$
Prove: $\triangle \mathrm{ROE} \sim \triangle \mathrm{REM}$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
00:57

Problem 26

Given: $\Varangle \mathrm{TRU}$ and $\mathrm{X.IRN}$ are vertical angles;
$$
\frac{\mathrm{RT}}{\mathrm{RI}}=\frac{\mathrm{RU}}{\mathrm{RN}}
$$
Prove: $\angle \mathrm{T}=\angle \mathrm{I}$
(GRAPH CANT COPY)

Christopher Stanley
Christopher Stanley
Numerade Educator
03:22

Problem 27

$$\begin{aligned}
&\text {Given: } \frac{\triangle \mathrm{TGN} \text { and } \Delta \mathrm{IGR}}{\mathrm{AE} \perp \overline{\mathrm{TN}} \text { and } \overline{\mathrm{AE}} \perp \overline{\mathrm{IR}}}{\text { with }}\\
&\text { Prove: } \frac{\mathrm{GA}}{\mathrm{GE}}=\frac{\mathrm{TN}}{\mathrm{IR}}
\end{aligned}$$
(GRAPH CANT COPY)

Debasish Das
Debasish Das
Numerade Educator