McDougal Littell Jurgensen Geometry : Student Edition 2000

Ray C. Jurgensen, Richard G. Brown

Chapter 4

Congruent Triangles - all with Video Answers

Educators

Section 1

Congruent Figures

Problem 1

Suppose $\triangle B I G \cong \triangle C A T .$ Complete.
$$\angle G \cong \frac{?}{}$$

Amrita Bhasin

Amrita Bhasin

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Problem 2

Suppose $\Delta B I G \cong \triangle C A T .$ Complete.
$$\frac{?}{}=m \angle A$$

Suzanne W.

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Problem 3

Suppose $\Delta B I G \cong \triangle C A T .$ Complete.
$$B I=?$$

Suzanne W.

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Problem 4

Suppose $\Delta B I G \cong \triangle C A T .$ Complete.
$$\frac{?}{} \equiv \overline{A T}$$

Ajay Singhal

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Problem 5

Suppose $\Delta B I G \cong \triangle C A T .$ Complete.
$$\triangle I G B \cong \frac{?}{}$$

Suzanne W.

Numerade Educator

Problem 6

Suppose $\Delta B I G \cong \triangle C A T .$ Complete.
$$\frac{?}{2} \cong \Delta C T A$$

Aman Gupta

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Problem 7

If $\triangle D E F \cong \triangle R S T, m \angle D=100,$ and $m \angle F=40,$ name four congruent angles.

Amrita Bhasin

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Problem 8

Is the statement "Corresponding parts of congruent triangles are congruent" based on a definition, postulate, or theorem?

Kashif Qureshi

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Problem 9

Suppose $\triangle L X R \cong \triangle F N E .$ List six congruences that can be justified by the following reason: Corr. parts of $\cong \Delta$ are $\cong$

Amrita Bhasin

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Problem 10

The two triangles shown are congruent. Complete.
a.$$\triangle S T O \cong \underline{?}$$
b. $$\angle S \cong \frac{?}{} \text { because } \frac{?}{}$$
c. $$S O \cong \frac{?}{}{} \text { because-$$?$$ }$$ Then point $O$ is the midpoint of $\underline{?}$
d. $$\angle T \cong \underline{?} \text { because } \underline{?}$$
$$\text { Then } \overline{S T} \| \overline{R K} \text { because } \underline{?}$$
(GRAPH CANT COPY)

Kashif Qureshi

Numerade Educator

Problem 11

The two triangles shown are congruent. Complete.
a. $\triangle P A L \cong \underline{?}$
b. $\overline{P A} \cong \frac{?}{}$
c. $\angle 1 \cong \underline{?}$ because $\underline{?}$ \text { Then } \overline{P A} \| \underline{?} \text { because } \underline{?}
$$Then\quad\overline{P A} \| \underline{?}=\text { because $\frac{?}{}$}$$
(GRAPH CANT COPY)
d. $$\angle 2 \cong \frac{?}{} \text { because } \underline{?}$$
\underline{?} \text { because } \underline{?}$$

Sheryl Ezze

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Problem 12

Plot the given points on graph paper. Draw $\triangle F A T$. Locate point $C$ so that $\triangle F A T \cong \triangle C A T$
$$F(1,2) \quad A(4,7) \quad T(4,2)$$

Kashif Qureshi

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Problem 13

Plot the given points on graph paper. Draw $\triangle F A T$. Locate point $C$ so that
$$\begin{aligned}
&F(7,5) \quad A(-2,2)\\
&T(5,2)
\end{aligned}$$

Amrita Bhasin

Numerade Educator

Problem 14

Plot the given points on graph paper. Draw $\triangle A B C$ and $\triangle D E F .$ Copy and complete the statement $\triangle A B C \cong ?$
$$\begin{aligned}
&A(-1,2) \quad B(4,2) \quad C(2,4)\\
&D(5,-1) \quad E(7,1) \quad F(10,-1)
\end{aligned}$$

Kashif Qureshi

Numerade Educator

Problem 15

Plot the given points on graph paper. Draw $\triangle A B C$ and $\triangle D E F .$ Copy and complete the statement $\triangle A B C \cong ?$
$$\begin{aligned}
&A(-7,-3) \quad B(-2,-3) \quad C(-2,0)\\
&D(0,1) \quad E(5,1) \quad F(0,-2)
\end{aligned}$$

Amrita Bhasin

Numerade Educator

Problem 16

Plot the given points on graph paper. Draw $\triangle A B C$ and $\triangle D E F .$ Copy and complete the statement $\triangle A B C \cong ?$
$$\begin{aligned}
&A(-3,1) \quad B(2,1) \quad C(2,3)\\
&D(4,3) \quad E(6,3) \quad F(6,8)
\end{aligned}$$

Naomi Siragusa

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Problem 17

Plot the given points on graph paper. Draw $\triangle A B C$ and $\triangle D E F .$ Copy and complete the statement $\triangle A B C \cong ?$
$$\begin{aligned}
&A(1,1) \quad B(8,1)\\
&C(4,3)\\
&D(3,-7) \quad E(5,-3) \quad F(3,0)
\end{aligned}$$

Amrita Bhasin

Numerade Educator

Problem 18

Plot the given points on graph paper. Draw $\triangle A B C$ and $\overline{D E}$. Find two locations of point $F$ such that $\triangle A B C \cong \triangle D E F$.
$$A(1,2) \quad B(4,2) \quad C(2,4) \quad D(6,4) \quad E(6,7)$$

Amrita Bhasin

Numerade Educator

Problem 19

Plot the given points on graph paper. Draw $\triangle A B C$ and $\overline{D E}$. Find two locations of point $F$ such that $\triangle A B C \cong \triangle D E F$.
$$A(-1,0) \quad B(-5,4) \quad C(-6,1) \quad D(1,0) \quad E(5,4)$$

Amrita Bhasin

Numerade Educator

Problem 20

$\overline{O R}$ is a common side of two congruent quadrilaterals.
Complete: quad. $N E R O \cong$ quad ?

Debasish Das

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Problem 21

$\overline{O R}$ is a common side of two congruent quadrilaterals.
In your own words explain why each of the following statements must be true.
a. $O$ is the midpoint of $\overline{N M}$.
b. $\angle N O R \cong \angle M O R$
c. $\overline{R O} \perp \overline{N M}$
(GRAPH CANT COPY)

Amrita Bhasin

Numerade Educator

Problem 22

Accurately draw each triangle described. Predict whether your triangle will be congruent to your classmates".
a. In $\triangle R S T, R S=4 \mathrm{cm}, m \angle S=45,$ and $S T=6 \mathrm{cm}$
b. In $\triangle U V W . m \angle U=30 . U V=5 \mathrm{cm} .$ and $m \angle V=100$
c. In $\triangle D E F . m \angle D=30 . m \angle E=68 .$ and $m \angle F=82$
d. In $\triangle X Y Z, X Y=3 \mathrm{cm} . Y Z=5 \mathrm{cm},$ and $X Z=6 \mathrm{cm} .$ (Try for a
reasonably accurate drawing. You may find it helpful to cut a thin strip of paper for each side. then form the triangle.)

Ashley High

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Problem 23

Does congruence of triangles have the reflexive property? the symmetric property? the transitive property?

Amrita Bhasin

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Problem 24

Suppose you are given a scalene triangle and a point $P$ on some line $l$ How many triangles are there with one vertex at $P,$ another vertex on $l$ and each triangle congruent to the given triangle?

AG

Ankit Gupta

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