Unit 4 - Triangle Relationships Review

Triangle Relationships Review

​Please have pen or pencil, and paper before you start this Final practice before tomorrow's exam.

Calculator

Multiple Choice

In similar Polygons, corresponding sides are ___ and corresponding angles are ___. (Fill in the blanks)

• congruent, proportional 

• congruent, congruent

• proportional, congruent

• proportional, proportional

​​Side Splitter Theorem - Left side ∼ Right side

Multiple Choice

The Side Splitter Theorem states that If a line is parallel to one side of a triangle and intersects the other two sides, then $$\frac{AB}{BC}=\frac{AE}{?}$$ ​ What is the question mark?

• BE

• AD

• CD

• ED

Multiple Choice

Given DE || BC, find AE.

• 12.5

• 11.75

• 18

• 13

Multiple Choice

Triangle PQT with RS is parallel to QT is shown below. If PR = 12, RQ = 8, and PS = 21, what is the length of PT ?

• 38

• 35

• 17

• 14

Multiple Choice

Find the value of x.

• x = 4.5

• x = 30

• x = 9

• x = 3

Multiple Choice

Solve for x.

• x = 8

• x = 7

• x = 9

• x = 5

Notice the Corresponding sides

Draw

In the diagram of ABC below, DE || BC, AD = 3, DB = 2, and DE = 6. Use 2 different colors to highlight the sides of the small inner Δ and of the Big outer Δ.

Multiple Choice

In the diagram of ABC below, DE || BC, AD = 3, DB = 2, and DE = 6. What is the length of BC?

• 12

• 10

• 8

• 4

Multiple Choice

In the diagram below of ABC, CDA, CEB,

DE is parallel to AB, DE = 4, AB = 10, CD = x, and

DA = x + 3. What is the length of AD?

• 9

• 8

• 6

• 2

Draw

Reminder!!!

$$AB=2\times DE\ or\ DE=\frac{1}{2}AB$$

CE = BE

AD = DC

Draw the ( ′ ) marks to show which lengths are congruent in the diagram.

Fill in the Blanks

Multiple Choice

Name a segment that has the same length as segment BD

• 
  segment BE

• segment AD

• segment DE

• segment AC

Multiple Choice

Is QR parallel to WU?

• yes

• no

Multiple Choice

QR is a midsegment of triangle WUV. What is the length of segment QR?

• 32

• 16

• 8

• 4

Multiple Choice

QR is a midsegment of triangle WXY. What is the length of segment WY?

• 3

• 6

• 9

• 12

Multiple Choice

QR is a midsegment of triangle BCD. Solve for the value of x.

• 11

• 9

• 18

• -7

Multiple Choice

IJ is a midsegment of triangle MLN. What is the length of segment IJ?

• $$\frac{3}{5}$$

• 4.5

• 6

• 9

Multiple Choice

VW is a midsegment of triangle KIJ. What is the length of segment KI?

• -1

• -10

• 8

• 18

Multiple Choice

Use the information in the diagram to determine the height of the tree.

• 80

• 40

• 360

• 180

​​Altitude Rule

​​Example

Multiple Choice

The Altitude of the given triangle is drawn in red. Find the value of x.

• 10

• 12

• 14

• 16

Multiple Choice

Find the value of x.

(diagram NOT DRAWN TO SCALE)

• $$4\ \sqrt[\ ]{2}$$

• $$\sqrt[]{32}$$

• 12

• 16

Multiple Choice

Find x.

• $$3\ \sqrt[]{7}$$

• $$2\ \sqrt[]{21}$$

• 10

• 20

Open Ended

In the given diagram of right triangle ABC, altitude BD intersects hypotenuse AC at D. If BD = 6,and DC = 18. What is the length of AD?

​Example

​Leg Rule

Multiple Choice

Using the Leg Rule, find the value of x.

• $$x=4\ \sqrt[]{3}$$

• $$x=2\ \sqrt[]{13}$$

• $$x\approx25$$

• $$x\approx24$$

Multiple Choice

Find the value of x.

• $$x=2\ \sqrt[]{15}$$

• $$x=2\ \sqrt[]{21}$$

• $$x=\sqrt[]{35}$$

Multiple Choice

Find the value of x.

• $$\sqrt[]{56}=2\ \sqrt[]{14}$$

• $$\sqrt[]{72}=6\ \sqrt[]{2}$$

• $$\sqrt[]{252}=6\ \sqrt[]{7}$$

• 14

Multiple Choice

To solve for x, do you use

Altitude Rule or Leg Rule?

• Altitude Rule

• Leg Rule

Example

Multiple Choice

As shown in the given diagram, AB and CD intersect at E, and AC || BD. If ΔAEC∼ ΔBED, which equation is true?

• $$\frac{CE}{DE}=\frac{EB}{EA}$$

• $$\frac{AE}{BE}=\frac{AC}{BD}$$

• $$\frac{EC}{AE}=\frac{BE}{ED}$$

• $$\frac{ED}{EC}=\frac{AC}{BD}$$

Multiple Choice

In the diagram, AD intersects BE at C, and AB || DE. If CD=6.6 cm, DE=3.4 cm, CE=4.2 cm, and BC=5.25 cm, what is the length of AC, to the nearest hundredth of a centimeter?

• 2.70

• 3.34

• 5.28

• 8.25

Multiple Choice

ΔABC ∼ ΔEDC and AB || ED. If CD = 3.5, what is the length of CB rounded to the nearest tenth?

• 9.6

• 4.9

• 10.5

• 8.4

Multiple Choice

As shown in the diagram, AB and CD intersect at E, and AC || BD. If AE = 7, EB = 5, AC = 3x + 5, and

BD = 2x + 4, what is the length AC

• 14

• 10

• 3

• 2

Proving a Right Triangle given Coordinate points.

Open Ended

ΔRST is graphed on the set of axes. Prove that ΔRST is a Right Triangle. You can take a picture of your work and upload it. Write your concluding statement below.