Name____________________________________ 14-1 Non-Negotiables Day 1

Geometry PD. ____

Geometry “Non-Negotiables”

The following are a list of topics and concepts that you must know, understand, and be able to answer

questions about, to be successful on the Geometry Regents Exam. It is essential that you have a

strong foundation in these topics before practicing and studying other topics and concepts from the

course, as these topics relate to many others and show up frequently throughout the Regents Exam.

1. Properties of Triangles

2. Median, Angle Bisector, Perpendicular Bisector, and Altitude Vocabulary

3. Angle Relationships

4. Equation of a Circle – by Completing the square

5. Properties of Quadrilaterals

6. Parallel and Perpendicular Lines

7. Pythagorean Theorem

8. Slope, Midpoint, Distance: The “BIG 3”

9. Methods to Prove Triangles Similar and Congruent

10. Rigid Motions

11. Cofunctions

12. SOHCAHTOA

13. Line Dilation

14. Scale factors

15. Partitions

16. SAASHLLS

17. Volume

18. Law of Sines/Law of Cosines

19. Circles

NN#1-I still need to

Review this topic

Non-Negotiable Examples #1-9

Work on the following non-negotiable items individually- DO NOT SKIP OVER ANY PROBLEMS- THESE

TOPICS WILL MOST LIKELY SHOW UP ON THE REGENTS AND WE HAVE TO MASTER THEM! Check

your work with the provided key ask questions if needed!

1. Properties of Triangles

The diagram below shows , with , , and .

If , what is ?

2. Median, Angle Bisector, Perpendicular Bisector, and Altitude Vocabulary In isosceles MNP, line segment NO bisects vertex MNP, as shown below. If MP = 16, find the length of MO and explain your answer.

3. Angle Relationships

In the diagram below, line is parallel to line m, and line w is a transversal.

If and , what is ?

NN#2-I still need to

Review this topic

NN#3-I still need to

Review this topic

4. Equation of a Circle – by Completing the square

The equation of a circle is . What are the coordinates of the center and the length of the radius of the

circle?

1) center and radius 4

2) center and radius 4

3) center and radius 16

4) center and radius 16

5. Properties of Quadrilaterals

In the diagram of parallelogram FRED shown below, is extended to A, and is drawn such that .

If , what is ?

1) 124°

2) 112°

3) 68°

4) 56°

6. Parallel and Perpendicular Lines Line m and point P are shown in the graph below.

Which equation represents the line passing through P and parallel to line m?

1)

2)

3)

4)

NN#4-I still need to

Review this topic

NN#5-I still need to

Review this topic

NN#6-I still need to

Review this topic

7. Pythagorean Theorem

An overhead view of a revolving door is shown in the accompanying diagram.

Each panel is 1.5 meters wide.

What is the approximate width of d, the opening from B to C?

1) 1.50 m

2) 1.73 m

3) 3.00 m

4) 2.12 m

8. Slope, Midpoint, Distance

The endpoints of one side of a regular pentagon are and . What is the perimeter of the pentagon?

1)

2)

3)

4)

9. Methods To Prove Triangles Are Similar And/Or Congruent

In the accompanying diagram, bisects and .

What is the most direct method of proof that could be used to prove ?

1)

2)

3)

4)

NN#7-I still need to

Review this topic

NN#8-I still need to

Review this topic

NN#9-I still need to

Review this topic

Mixed Practice – What isn’t completed is homework. You must check with key online

1. Write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,8) and (5, 4).

2. A regular hexagon is shown in the diagram below. If the hexagon is rotated clockwise around its center, find the minimum number of degrees it must be rotated to map the hexagon onto itself.

3. In , , , and . What is the value of x? What is the largest side of the triangle?

4. An equation of a line perpendicular to the line represented by the equation and passing through is

1)

2)

3)

4)

5. In parallelogram QRST shown below, diagonal is drawn, U and V

are points on and , respectively, and intersects at W.

If , , and , what is ?

6. Quadrilateral ABCD has diagonals and . Which information is not sufficient to prove ABCD is a parallelogram?

1) and bisect each other.

2) and

3) and

4) and

7. What are the coordinates of the center and length of the radius of the circle whose equation is ?

The diagram below shows a pennant in the shape of an isosceles triangle. The equal

sides each measure 13, the altitude is , and the base is 2x.

What is the length of the base?

1) 5

2) 10

3) 12

4) 24

8. In the diagram below, parallelogram ABCD has vertices , , , and . Diagonals and

intersect at E.

What are the coordinates of point E?

9. In the diagram below, has vertices , , and .

What is the slope of the altitude drawn from A to ?

1)

2)

3)

4)

10. Performance Non-Negotiable! GET A COMPASS ALWAYS HAVE IT!

11. In the diagram of below, , , , and .

What is the length of , to the nearest tenth?

1) 5.1

2) 5.2

3) 14.3

4) 14.4

12. In the accompanying diagram of right triangles ABD and DBC, , , and .

Find the length of , leave answer in simplest radical form.