Name: _______________________________ Date: ______________Geometry Per _______ Midterm – Extra Practice

UNIT 1

1. REFLECTIONS: Write the image of A(3,4) under the following reflections:

rx-axis(x,y) = ry-axis(x,y) = ry=x (x,y) = ry=-x (x,y) =

ROTATIONS: Write the image of A(5,2) under the following rotations: (Turn your paper)!

R90(x,y) = R180(x,y)= R270(x,y) = R-90(x,y) =

GLIDE REFLECTIONS KEY IDEAS:

-What 2 transformations are used in a glide reflection?

-How do we check if we have a glide reflection?

2. Graph triangle ABC. A(1, 1), B(4, 5), C(3, 2) and reflect it through point (-2, 1)

A(1, 1) →

B(4, 5) →

C(3, 2) →

3. Graph and state the coordinates of ∆ A ' B 'C ' , the image of ∆ ABC after the composition T 2,0o R180 °.Show your work!

4. Consider the regular octagon below. What is the least amount of degrees you must rotate the octagon so that it maps onto itself?

UNIT 2

CONSTRUCTIONS

Using the word bank, label each construction shown below!

Angle Bisector Parallel Lines Perpendicular Line Through a point

Perpendicular Bisector Equilateral Triangle

A(2,1)

B(4,7)

C(6,8)

UNIT 3

1. Are the two lines represented below parallel, perpendicular or neither? JUSTIFY your answer.

Equation 1: y−5=45

( x+2 )

Equation 2: y−2=45(x+5)

2. Write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,8) and (11, -4)

3. Line segment AB has endpoints A(2, 8), and B(-2, 2). Line segment CD has endpoints C(6, 3) and D(-6, 7). Do ABand CD bisect each other?

4. Line segment JK has endpoints J(0,0) and K(12, 9). Line segment UV has endpoints U(2, 3) and V(5, 7). Which segment is longer (has a greater length)?

5. In the diagram below, line p intersects line m and line n. If and , lines m and n are parallel when x equals

1) 12.5

2) 15

3) 87.5

4) 105

6. Solve for x, given that the two lines cut by a transversal are parallel, and ¿1=x+10 and ¿7=2x−40.

7. A linear pair of angles are in a 3:6 ratio. Find each angle.

UNIT 4

1. The diagram at the right shows a right triangle with representations for two angles. What is the value of x?

2. In triangle DOG, m<D = 40, m<O 60, and m<G = 80.

State the longest side of the triangle: ______________

State the shortest side of the triangle: ______________

3. State whether each of the following could be the sides of a triangle and why.

a) {6,6,6} b) {2,2,4}

4. Two sides of a triangle have lengths 2 and 7. Write an inequality for all possible integer lengths of the third side.

5. In the diagram below of quadrilateral ABCD with diagonal , , , , and

. If is parallel to , find m ¿ ABD.

6. Determine whether the following sides form a right , acute or obtuse triangle. Justify your answer with words.

a) 5, 11, 12 b) 5, 12, 13

7.

8. Solve for x . Give your answer in the simplest radical form.

9. Find the coordinates of the centroid of the triangle with the given vertices.

J(−1, 2), K(5, 6), L(5, −2)

10. a) What is the sum of the exterior angles of regular decagon?

b) Find one of the exterior angles.

11. a) What is the sum the interior angles of a regular nonagon (9 sides).

b) Find the measure of one interior angle of a regular nonagon.

UNIT 5

1.

Statements Reasons

2.

Prove ∠ ABC≅ ∠ ADC

3. Read the proof below and fill in the missing statements and reasons.

Given: C is the midpoint of line segments AY and BX . Prove: ΔBCA ≅ Δ XCY

Statements Reasons

1. 1. Given

2. BC ≅ XC 2.

3. 3. A midpoint divides a segment into two equal parts

4. 4.

5. ΔBCA≅ Δ XCY 5.

4. In the diagram below of , .

Statements Reasons

Using this information, it could be proven that

1) 3)

2) 4)

WHAT POSTULATE DID YOU USE TO ANSWER THE QUESTION ABOVE? __________________________________

UNIT 6

1. Which of the following represents ∆ ABC undergoing a rotation of 90 counterclockwise about point C followed by a reflection over the x-axis? (2 points)

1) r x−axis¿(∆ ABC ¿¿

2) r x−axis¿(∆ ABC ¿¿

3)R x−axis¿(∆ ABC ¿¿

4)RC ,−90¿(∆ ABC ¿¿

2. Given: G is the image of E after a reflection over DF and ΔDEF and ΔDGF are drawn.

Prove using rigid motions: ΔDEF≃ΔDGF (6 points)

Statements Reasons

1. G is the image of E after a reflection over DFand,ΔDEF and ΔDGF are drawn.

1. Given

2. 2.

3. 3.

4. 4.

3. The triangles ∆ ABC and ∆≝¿ in the figure below such that AB≅ DE, CB≅ FE, and ∠B∧∠E are right angles. Describe a sequence of rigid transformations thatshows ∆ ABC ≅∆≝¿. (3 points)

4. Given: ¿ Z≅<X , WY is and angle bisector of ∠W. Prove: ∆ ZWY ≅∆ XWY (4 points)

UNIT 7

1. Given: Quadrilateral ABCD with A( - 5, 0), B(1, –4), C(5, 2), D(–1, 6).Prove: ABCD is a rectangle.

2. Prove Quadrilateral ABCD is a rhombus with coordinates: A(-3,2), B(-2,6), C(2,7)and D(1,3).

3. Prove that quadrilateral A(1,-2), B(13,4), C(6,8) and D(-2,4) is a trapezoid, but is NOT an isosceles trapezoid.

4. Given that CATS is a rhombus, solve for m∠CST .

5. In the accompanying diagram of parallelogram ABCD, m∠D=10 x−10 and m∠B=8 x. Find the number of degrees in m<A.

6. In isosceles trapezoid CATS with legs CA and TS, CA = 3x-2, AT = 2x +7, TS = 5x +9, andSC = 5x -2. Find the value of x.

7.a) Given quadrilateral SING is a rhombus with diagonals SN and IG, ∠ SNG = 3x and ∠NGI=6 x, solve for

∠ ING .

b) Using the diagram above, where SE = 2y, EN = 6y - 8, IE = y, solve for the length of each diagonal.