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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 .