Final Exam Review

Pythagorean Theorem

By Dana Kuramoto

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Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• YES

• NO

Multiple Choice

Is this a right triangle?

• YES

• NO

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Similarity in Right Triangles

by Deb Scott

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Objective: Find and Use relationships in similar right triangles.

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Multiple Select

What does it mean when triangles are similar?

More than one correct answer

• corresponding angles are congruent

• corresponding sides are congruent

• corresponding sides are proportional

• I have no clue

Multiple Select

What is a possible equation for solving for y?

more than one correct answer

• $$\frac{12}{y\ }=\frac{y}{4}$$

• $$\frac{12}{4}=\frac{y}{x}$$

• $$\frac{4}{y\ }=\frac{y}{12}$$

• $$\frac{x}{4\ }=\frac{12}{x}$$

• y = 48

Multiple Choice

Solve for y. Leave in simplest radical form

• $$\sqrt[]{48}$$  

• $$4\sqrt[]{3}$$  

• $$3\sqrt[]{4}$$  

Multiple Select

What is a possible equation for solving for x?

more than one correct answer

• $$\frac{4}{x\ }=\frac{x}{16}$$

• $$\frac{4}{x\ }=\frac{x}{12}$$

• $$\frac{16}{x\ }=\frac{x}{4}$$

• $$\frac{x}{4}=\frac{4}{y}$$

Multiple Choice

Solve for x.

Leave in simplest radical form

• 8

• 10

• 64

• $$4\sqrt[]{3}$$  

Geometric Mean is an average which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

Multiple Choice

Find the missing length indicated.

• 60

• 100

• 80

• 20

Multiple Choice

Find the missing length indicated.

• 64

• 12

• 9

• 100

Multiple Choice

• 10
• 12
• 14
• 16

Special Right Triangles

Review

Multiple Choice

• a=√6   b=√2
• a=4   b=2
• a=√6   b=2
• a=2   b4

Multiple Choice

Use the 45-45-90 theorem to solve for the hypotenuse.

• 16

• 8

• 8√2

• √16

Multiple Choice

Find x - the length of the hypotenuse of the triangle.

• 5
• 5√2
• 10
• 5√3

Solving Right Triangles

Pythagorean Theorem​

• When a problem involves only sides, use Pythagorean Theorem

Trigonometry

• When a problem involves both sides and angles, use SOH-CAH-TOA

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa
• Soh Cah Toa
• Soh Cah Tao
• Soh Ceh Toa

Multiple Choice

What is

$$\tan\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

What is

$$\cos\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

What is

$$\sin\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14
• sin(33)=x/14
• cos(33)=14/x
• sin(33)=14/x

Multiple Choice

Find the value of x.

• 8.43

• 11.18

• 10.55 

• None of these are correct

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

Multiple Choice

What is the correct set up for the problem to solve for side w?

• $$\sin\left(40\degree\right)=\frac{w}{28}$$  

• $$\cos\left(40\degree\right)=\frac{w}{28}$$  

• $$\tan\left(40\degree\right)=\frac{w}{28}$$  

• $$\sin\left(40\degree\right)=\frac{28}{w}$$  

Multiple Choice

What is the length of side "w?"

• 18.0 

• 21.4

• 23.5

• 43.56 

 Inverse trig is used to find missing angles. 

• sin^-1 (sometimes called arcsin or sinh on your phone calculators)

•  cos^-1 (sometimes called arccos or cosh)

•  tan^-1 (sometimes called…you guessed it…arctan or tanh)

How do we use Trig Functions to find missing angles?

• Step 1: Identify the angle

• Step 2: Label opp, adj, and hyp based on given angle

• Step 3: Identify the appropriate trig function to solve for the missing angle

• Step 4: Use sin^-1 , cos^-1 , tan^-1 to solve the equation for the angle 

Multiple Choice

To find a missing angle when given two sides, you must use ______

• Trigonometric Functions

• Trigonometric Rations

• Inverse Trigonometric Functions

• Pythagorean Theorem

Multiple Choice

Choose the correct ratio.

• sin^-1(9/20)

• cos^-1(9/20)

• tan^-1(9/20)

• cos^-1(20/9)

Multiple Choice

Find the measure of the angle. Round to the nearest tenth.

• 30.8

• 32.1

• 34.3

• 36.9

Multiple Choice

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

• 49°

• 57°

• 45°

• 54°

Multiple Choice

What is the SUM of the exterior angles of a 20-gon?

• 180

• 360

• 3240

• 162

Multiple Choice

Find the value of y.

• 125
• 135
• 140
• 110

Multiple Choice

Find the angle SUM of the interior angles of the polygon.

• 180°

• 540°

• 720°

• 1080°

Multiple Choice

Find the value of X

• 94
• 25
• 36
• 180

Properties of Parallelograms

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. 

Parallelogram Conjecture #1

 

Opposite sides of a parallelogram are congruent.

Multiple Choice

The figure is a parallelogram.

Solve for x.

• 4

• 12

• 5

• 2

Parallelogram Conjecture #2

Opposite angles of a parallelogram are congruent.

Multiple Choice

Solve for y.

• $$70\degree$$

• $$110\degree$$

Multiple Choice

• FG = 6, m<G = 120

• FG = 16, m<G = 60

• FG = 8, m<G = 60

• FG = 7, m<G = 65

Parallelogram Conjecture #3

Multiple Choice

The figure is a parallelogram.

Solve for x.

• 1

• 10

• 4

• 5

Parallelogram Conjecture #4

The diagonals of a parallelogram bisect each other.

Multiple Choice

If DB = 20, find DE.

• 5

• 10

• 20

• 40

Please read each definition and study the image associated with it.

Multiple Choice

In rectangle RSBF, SF = 2x + 15 and RB = 5x - 12. What is the length of one diagonal?

• 1

• 9

• 18

• 33

Poll

A parallelogram with four congruent sides is a

• rhombus

• square

• rectangle

Poll

A parallelogram with four right angles is a

• rhombus

• rectangle

• square

Multiple Choice

What is the measurement of <1

• 58

• 90

• 116

• 32

Multiple Choice

What is the measurement of < 3

• 58

• 90

• 116

• 32

Multiple Choice

What is also true about <2, <3, and <4?

• They are all 104 degrees

• They are are 76 degrees

• They are all 38 degrees

Multiple Choice

In rectangle RSBF, SF = 2x + 15 and RB = 5x - 12. What is the length of a diagonal?

Hint: SF and RB are diagonals.

• 1

• 9

• 18

• 33

Multiple Choice

What is the best name for this picture?

• rectangle

• square

• rhombus

• parallelogram

Multiple Choice

What is the best name for this picture?

• rhombus

• rectangle

• square

• parallelogram

Multiple Choice

What is the best name for this picture?

• parallelogram

• rhombus

• square

• rectangle

Multiple Choice

 What is the best name for this picture?

• rectangle

• rhombus

• square

• parallelogram

​Vocabulary

Isosceles Trapezoid

• An isosceles trapezoid has a few more unique properties...

• "Base" angles are congruent (A and D; B and C)

• Diagonals are congruent

Multiple Choice

Select the correct values of x and y

• x=56, y=56

• x=56, y=124

• x=124, y=56

• x=124, y=124

Midsegment of Trapezoids

Multiple Choice

Find $$x$$  

• 12

• 13

• 19

• 26

​Vocabulary

Kites

• Quadrilateral ABCD at the right is a kite

• Kites have two pairs of congruent adjacent sides (congruent sides are next to each other)

• Kites also have ONE pair of congruent angles

• Kites are symmetric down the middle

Multiple Choice

Find $$m\angle A$$  

• 81

• 118

• 99

• 62

Diagonals of a Kite

When the diagonals are drawn in a kite, they form four right angles. Therefore the diagonals of a kite are perpendicular.

One diagonal also bisects the other.

Multiple Choice

Find the value of 2x-7.

• 7.5

• 8

• 11

• 15

Multiple Choice

Find y.

• 42
• 7
• 6
• 180

Multiple Choice

Find v.

• 81
• 4
• 27
• 90

​Types of Quadrilaterals Flow Chart

Multiple Choice

$$m\angle2=?$$

• 55

• 125

• 110

• 27.5

Multiple Choice

$$m\angle3=?$$

• 55

• 125

• 110

• 27.5

Multiple Choice

$$XY=?$$

• 12

• 4

• 24

• 10

Multiple Choice

GLOT is a kite.   $$x=?$$  

• 4

• 2

• 5.5

• 3

Multiple Choice

$$m\angle3=?$$

• 63

• 27

• 90