Question 1

In the diagram below of right triangle $ABC$, altitude $\overline {BD}$ is drawn to hypotenuse $\overline {AC}$.
If $BD=4, AD=x-6$, and $CD=x$, what is the length of $\overline {CD}$?

Accepted Answer

8

Answer

11

Answer

2

Answer

5

Question 2

In the diagram of $\Delta ABC$ below, points $D$ and $E$ are on sides $\overline {AB}$ and $\overline {CB}$ respectively, such that $\overline {DE} \parallel \overline{AC}$.

If $EB$ is 3 more than $DB, AB=14$, and $CB=21$, what is the length of $\overline {AD}?$

Accepted Answer

8

Answer

9

Answer

6

Answer

12

Question 3

In triangle $ABC$, points $D$ and $E$ are on sides $\overline{AB}$ and $\overline {BC}$, respectively, such that $\overline {DE} \parallel \overline {AC}$, and $AD:DB=3:5$.

If $DB=6.3$ and $AC=9.4$, what is the length of $\overline {DE}$, to the $nearest tenth?$

Accepted Answer

5.9

Answer

5.6

Answer

15.7

Answer

3.8

Question 4

In the diagram below of circle $O$, points $K,A,T,I$ and $E$ are on the circle, $\Delta KAE$ and $\Delta ITE$ are drawn, $\stackrel \frown{KE} 
 \cong \stackrel \frown{EI}$, and $\angle EKA \cong \angle EIT$.

Accepted Answer

They are congruent.

Answer

They are similar but not congruent.

Answer

They are neither congruent nor similar

Answer

They are right triangles.

Question 5

In right triangle $ABC$ shown below, point $D$ is on $\overline {AB}$ and point $E$ is on $CB$ such that $\overline {AB} \parallel \overline {DE}$.
If $AB=15,BC=12$, and $EC=7$, what is the length of $\overline{BD}$

Accepted Answer

6.25

Answer

8.75

Answer

4

Answer

5

Question 6

Given right triangle $ABC$ with a right angle at $C$, $m\angle B=61\degree$. Given right triangle $RST$ with a right angle at $T$, $m\angle R=29\degree $.

Which proportion in relation to $\Delta ABC$ and $\Delta RST$ is $not$ correct?

Accepted Answer

$\frac {AB}{RS}= \frac {RT}{AC}$

Answer

$\frac {AB}{AC}= \frac {RS}{RT}$

Answer

$\frac {BC}{ST}= \frac {AC}{RT}$

Answer

$\frac {BC}{ST}= \frac {AB}{RS}$

Question 7

In the diagram below of right triangle $KMI$,  altitude $\overline {IG}$ is drawn to hypotenuse $\overline {KM}$.

If $KG=9$ and $IG=12$, the length of $\overline {IM}$ is

Accepted Answer

20

Answer

16

Answer

15

Answer

25

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