Geometry

Harold R. Jacobs

Chapter 4

Congruent Triangles - all with Video Answers

Educators

Section 1

Triangles

Problem 1

The following exercises refer to $\triangle \mathrm{JAN}$, in which $\mathrm{JA}=\mathrm{JN}$.
What kind of triangle is $\triangle J A N$ with respect to its sides?

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Problem 2

The following exercises refer to $\triangle \mathrm{JAN}$, in which $\mathrm{JA}=\mathrm{JN}$.
What kind of triangle is $\triangle J$ AN with respect to its angles?

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Problem 3

The following exercises refer to $\triangle \mathrm{JAN}$, in which $\mathrm{JA}=\mathrm{JN}$.
Name its vertices.

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Problem 4

The following exercises refer to $\triangle \mathrm{JAN}$, in which $\mathrm{JA}=\mathrm{JN}$.

Name its legs.

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Problem 5

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
What kind of triangle is $\triangle \mathrm{FEB}$ with respect to its sides?

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Problem 6

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
What kind of triangle is $\triangle \mathrm{FEB}$ with respect to its angles?

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Problem 7

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
Name the sides of the triangle that include $\Varangle \mathrm{F}$

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Problem 8

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
Name the side opposite $\Varangle \mathrm{E}$.

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Problem 9

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
Name the angle opposite side $\overline{\mathrm{EF}}$.

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Problem 10

The following exercises refer to $\triangle \mathrm{FEB}$, which has no equal sides.
Name the angles that include side $\overline{\mathrm{FB}}$.

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Problem 11

The following exercises refer to $\triangle \mathrm{MAY}$, in which $\Varangle Y$ is a right angle.
What kind of triangle is $\triangle$ MAY with respect to its sides?

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Problem 12

The following exercises refer to $\triangle \mathrm{MAY}$, in which $\Varangle Y$ is a right angle.
What kind of triangle is $\triangle$ MAY with respect to its angles?

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Problem 13

The following exercises refer to $\triangle \mathrm{MAY}$, in which $\Varangle Y$ is a right angle.
Name its legs.

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Problem 14

The following exercises refer to $\triangle \mathrm{MAY}$, in which $\Varangle Y$ is a right angle.
Name its hypotenuse.

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Problem 15

Review the definitions of isosceles and equilateral triangles before answering the following questions.
If a triangle is equilateral, is it also isosceles?

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Problem 16

Review the definitions of isosceles and equilateral triangles before answering the following questions.
Why or why not?

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Problem 17

Review the definitions of isosceles and equilateral triangles before answering the following questions.
If a triangle is isosceles, is it also equilateral?

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Problem 18

In the figure at the top of the next column, M-H-R and C-H-A. Name all of the triangles in the figure that have each of the following as one of their parts.
(FIGURE CAN'T COPY)
$$\overline{\mathrm{MR}}$$

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Problem 19

In the figure at the top of the next column, M-H-R and C-H-A. Name all of the triangles in the figure that have each of the following as one of their parts.
(FIGURE CAN'T COPY)
$$\overline{\mathrm{AR}}$$

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Problem 20

In the figure at the top of the next column, M-H-R and C-H-A. Name all of the triangles in the figure that have each of the following as one of their parts.
(FIGURE CAN'T COPY)
$$\measuredangle {CHR}$$.

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Problem 21

In the figure at the top of the next column, M-H-R and C-H-A. Name all of the triangles in the figure that have each of the following as one of their parts.
(FIGURE CAN'T COPY)
$$\measuredangle {AMR}$$.

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Problem 22

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
Which two triangles in the figure are right triangles?

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Problem 23

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
Which triangle is an acute triangle?

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Problem 24

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
Which two triangles are obtuse triangles?

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Problem 25

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
How many angles in the figure have their vertex at L?

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Problem 26

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
How many angles in the figure have their vertex at $\mathrm{P} ?$

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Problem 27

$$\text { In the figure below, } \overline{\mathrm{PI}} \perp \overline{\mathrm{LR}} \text { . }$$.
(DIAGRAM CAN'T COPY)
How many angles in the figure can be named with just one letter?

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Problem 28

Use a straightedge to draw an example of each type of triangle in the table that you think can exist. If you think the figure cannot exist, write "impossible."

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Problem 29

Use your ruler and protractor to draw triangles having the following parts.
$$\begin{aligned}
&\triangle \mathrm{AUG}, \text { in which } \mathrm{AG}=5 \mathrm{cm}, \angle \mathrm{A}=60^{\circ}\\
&\text { and } \mathrm{AU}=3 \mathrm{cm}
\end{aligned}$$

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Problem 30

Use your ruler and protractor to draw triangles having the following parts.
$$\begin{aligned}
&\triangle \mathrm{OCT}, \text { in which } \angle \mathrm{O}=60^{\circ}, \mathrm{OT}=3 \mathrm{cm}\\
&\text { and } \angle \mathrm{T}=95^{\circ}
\end{aligned}$$

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Problem 31

Use your ruler and protractor to draw triangles having the following parts.
$$\begin{aligned}
&\triangle \mathrm{NOV}, \text { in which } \mathrm{NV}=3 \mathrm{cm}, \angle \mathrm{V}=60^{\circ}\\
&\text { and } \mathrm{VO}=3 \mathrm{cm}
\end{aligned}$$

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Problem 32

Use your ruler and protractor to draw triangles having the following parts.
$$\begin{aligned}
&\triangle \mathrm{DEC}, \text { in which } \angle \mathrm{D}=95^{\circ}, \mathrm{DC}=3 \mathrm{cm}\\
&\text { and } \angle \mathrm{C}=60^{\circ}
\end{aligned}$$

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Problem 33

Use your ruler and protractor to draw triangles having the following parts.
How many parts of each triangle did you need to be able to draw it?

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Problem 34

Refer to your drawings to answer the following questions. (You may need to make some measurements.)
Tell, using two words, what type of triangle each of your figures appears to be.

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Problem 35

Refer to your drawings to answer the following questions. (You may need to make some measurements.)
Name the two triangles that seem to have the same size and shape.

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