Geometry SOL Review Packet · 2019-05-08 · 8. Solve for x. 9. Solve for x. 10. In this figure, parallel lines a and b are intersected by line c. Which pair of angles is NOT supplementary?

Geometry SOL Review Packet

LT 1: Foundations of Geometry

Quiz Grade _______ Section Complete? _______

LT 2: Slope and Equations of Lines

Quiz Grade _______ Section Complete? _______

LT 3: Parallel Lines and Transversals

Quiz Grade _______ Section Complete? _______

Formula Review

Section Complete? _______

Name ______________________________________________ Period _________

**If found, PLEASE return me to Ms. Wilhelm, Room 2502

LT 1 – Foundations of Geometry

Important Concepts to Know

Complementary Angles

Linear Pairs

Supplementary Angles

Vertical Angles

Examples of SOL-Like Questions 1. Use the picture given to name an example of each vocabulary word. Point Line Line Segment Ray

1.

2. Suppose point K is between J and L, and J, K, & L are collinear. JK = 3x +8, KL = 2x – 5, JL = 23. Find KL.

3.

4. In △ABC, m∠A = x, m∠B = 2x + 2, and m∠C = 3x + 4. What is the value of x?

5.

6.

7.

8. Give the measure of two supplementary angles if the difference between their measures is 18 degrees.

LT 2 – Slope

Important Concepts to Know

What is slope?

Equation of a Line

Parallel Lines

Perpendicular Lines

Examples of SOL-Like Questions 1.

2.

3.

4.

5. Graph the line x = -2

6. Which of the following equation(s) are perpendicular to the equation?

y = - 1

3 x + 2

Circle ALL that apply

a) y = - 1

3 x + 6 b) y =

1

3 x + 1 c) y = 3x - 5

d) y = -3x e) y = 3x + 2

7. What is the slope of a line perpendicular to AB?

8. Given the graph of the line on the left, find the coordinates of one point that is on the perpendicular to the given line that goes through the point (-1, -4).

LT 3 – Parallel Lines & Transversals

Important Concepts to Know

Angle Relationships

Adjacent Angles (≅ -or- add to 180o)

<1 and ________

_______ and ________

Alternate Interior (≅ -or- add to 180o)

<4 and ________

_______ and ________

Consecutive Interior (≅ -or- add to 180o)

<2 and ________

_______ and ________

Alternate Exterior (≅ -or- add to 180o)

<6 and _______

_______ and ________

Linear Pairs (≅ -or- add to 180o)

<5 and _______

_______ and ________

Examples of SOL-Like Questions 1. Which lines are ||?

a) k and m b) k and n c) k and p d) m and n

2. Based on the diagram below, which statement is true?

A.

B.

C.

D.

k mn p

75

105

75

105

3.

5. In the diagram 𝐹𝐴𝐵𝐺̅̅ ̅̅ ̅̅ ̅̅ ∥ 𝐻𝐶𝐷𝐼̅̅ ̅̅ ̅̅ ̅, 𝐵𝐶̅̅ ̅̅ and 𝐴𝐷̅̅ ̅̅ intersect at E, m∠GBE = 3x + 20 and m∠ECD = x. What is the value of x?

6. Find the measure of ∠𝐵𝐸𝐶.

7.

A)

B)

C)

D)

8. Solve for x.

9. Solve for x.

10. In this figure, parallel lines a and b are intersected by line c.

Which pair of angles is NOT supplementary? A ∠ 1 and ∠ 6

B ∠ 3 and ∠ 8

C ∠ 2 and ∠ 7

D ∠ 4 and ∠ 6

11. This figure shows parallel stair railings through points M, N, P, and Q.

What is the value of x? A 29

B 45

C 61

D 119

12. The figure represents a ramp with handrails. Segments AB and DE are parallel to 𝐺𝐻̅̅ ̅̅ . Segments BC and EF are parallel to 𝐻𝐽̅̅̅̅ . Segments AG and BH are parallel to 𝐶𝐽̅̅ ̅.

If m∠JCB = 115°, what is m∠CBA ? A 65°

B 90°

C 115°

D 155°

13. Which diagram shows a pair of angle measures that prove line a and b are parallel?

14. The figure shows 𝐽𝑁̅̅̅̅ and 𝐾𝑀̅̅ ̅̅ ̅ intersecting at point 𝐿.

What value of 𝑥 proves 𝐽𝐾̅̅ ̅||𝑀𝑁̅̅ ̅̅ ̅?

15. Choose the best answer.

In the drawing above, <4 and <12 are

A.) alternate interior angles B.) consecutive interior angles C.) corresponding angles D.) a linear pair

16. A diagonal walkway cuts through a park bordered by two parallel streets. The parks department plans to add an additional walkway as indicated by the dashed line segment in the figure.

What is the value of 𝑥? A. 42 B. 48 C. 90 D. 138

NEED TO KNOW: SOL Formulas!!!

Coordinate Formulas

Slope = Parallel lines have the _______ slopes Perpendicular lines have ______________, _____________ slopes Midpoint = ( , ) Pythagorean Theorem = When do we use the Pythagorean Theorem?

Transversals

Name the transversal: _____

Relationship Examples 1. Corresponding 2. Alternate Interior 3. Alternate Exterior 4. Consecutive Interior

5. Vertical 6. Linear Pair

Angles colored the same are ______________ Angles colored differently are _____________

Triangle Inequalities

Will it form a triangle? - The sum of any two sides of a triangle must be ________________ the third side

Finding the range of the third side: _______ and ___________ the given two sides ____________ < x < ___________

Triangles and Angles

𝑚∠1 + 𝑚∠2 + 𝑚∠3 = _________

𝑚∠2 + 𝑚∠3 = 𝑚∠ ____

𝑚∠1 + 𝑚∠4 = ________

𝑚∠4 + 𝑚∠5 + 𝑚∠6 = ________

1

2

3 4

5

6

_________ side

_________

Angle

__________ Angle

________ Side

Triangle Postulates

Two triangles are congruent if… •

•

•

•

•

Two triangles are similar if… •

•

•

Trigonometry Must be in ____________ Mode!!! The Acronym: Ratios: sin = cos = tan =

Polygons Number of sides =

Sum of all interior angles (SI)

Sum of all exterior angles (SE)

One interior angle (I) One exterior angle (E)

Proportions in Similar Figures LAV Chart:

Ratio is the same as ______________ ______________, which includes:

Quadrilateral Flow Chart

A

____

____

____

____

____

____