Geometry Performance Expectations by Reporting Strand

Geometry Performance Expectations by reporting Strand

Reporting Strands / Performance Expectations / Anticipated number of questions
Logical arguments and proof / G.1.D
G.1.E
G.1.F / 6-8
Proving and applying properties of 2-dimensional figures / G.3.A
G.3.B
G.3.C
G.3.D
G.3.E
G.3.F
G.3.G / 21-24
Figures in a coordinate plane and measurement / G.4.B
G.4.C
G.6.E
G.6.F / 7-9
Course-Specific content / G.1.A
G.2.A
G.2.B
G.2.C
G.2.D
G.3.B
G.3.H
G.3.I
G.3.J
G.3.K
G.4.A
G.4.D
G.5.A
G.5.B
G.5.C
G.5.D
G.6.A
G.6.C
G.6.D / 6*
Question / PE / Answer

1. Determine the value of x if ΔABC is equilateral.

Write your answer on the line. / G.3.A /

1. Write the converse of the conditional statement. Determine if the converse is true or false. If it is false, find a counterexample.

“If you have a dog, then you are a pet owner.” / G.1.D / C: If you are a pet owner, then you have a dog. False, you could have a hamster.

1. Given a║b, determine which equation must be true.

/ G.2.B / D: m4 + m6 = 180

1. Determine measure of angle 2.

Write your answer on the line.
/ G.3.A / m2=50˚

1. ΔDEF has vertices D(4, 1), E(2, –1), and F(–2, –1). Classify ΔDEF based on its sides.

/ G.4.C / C: scalene

1. Determine the equation of a line through the point (3, –4) that is perpendicular to the line y = 3x + 7.

/ G.4.A / C:

1. Joe and Sara were standing on a pier sailing a toy sail boat. The boat was 6 feet from the base of the pier and the pier was 4 feet above the water.

Determine the angle of depression from the pier to the toy sail boat.
Show your work using words, numbers and/or diagrams. / G.3.A / ˚

1. Joanna’s teacher said “The diagonals of a square bisect each other.”

Joanna drew this figure and said “The diagonals of this figure bisect each other, so it must be a square.”

Joanna made an error in her mathematical argument. What is the error? / G.1.E / B: In the figure Joanna drew, the diagonals do not bisect each other.

1. Determine the midpoint of , where J(–1, 2) and K(6, 8).

/ G.4.B / B: (, 5)

1. Look at the diagram.

What theorem or postulate can you use to prove ? / G.3.B / C: Angle-Side-Angle Congruence

1. Three vertices of a square have coordinates (3, 1), (4, -4) and (-1, -5). The diagonals of the square intersect at point Q.

Determine the coordinates of point Q. / G.4.B / Q (1, -2)

1. 3, 5, 7, and 11 are prime numbers. 4, 6, 8, 9, and 10 are composite numbers. Tiana makes the conjecture that prime numbers must be odd.

Which statement is true? / G.1.A / B: This is an example of inductive reasoning and the conjecture is not valid.

1. One leg of a triangle is 8 cm long.

Determine the length of the hypotenuse. / G.3.C / B:

1. Look at the conditional statement.

“If an angle measures 30, then it is acute”
Which statement is the converse? / G.1.D / C: If an angle is acute, then it measures 30.

1. Which equation represents the line through the points (-1, -2) and (2, 7)?

/ G.4.A / A: y = 3x + 1

1. Which statement is true about all parallelograms?

/ G.3.F / C: The diagonals bisect each other.

1. Quadrilateral ABCD is a rhombus and m∠BCE = 50.

Determine the m∠EBC. / G.3.G / m∠EBC=40˚

1. Look at the conditional statement.

“If a figure is a pentagon, then it has five sides”
Which statement is the inverse? / G.1.D / D: If a figure is not a pentagon, then it does not have five sides.

1. Triangle JKE is an obtuse isosceles triangle with m∠E = 10and .

What is the m∠J? / G.3.A / B: 160

1. A proof is shown.

Fill in the blanks for steps 5 and 6 to complete the proof.
Given: B is the midpoint of .
B is the midpoint of .
Prove:. / G.3.B / Statement 5: m∠ABD=m∠CBE
Reason 6: SAS congruency

1. Which ordered pair is the midpoint of the line segment with endpoints

(2,-5) and (-6, 4)? / G.4.B / C:

1. The diagonal of a square is 7 cm.

Determine the length of one side of the square. / G.3.C / D:

1. Which statement is true?

/ G.1.F / A: A postulate is accepted as true without proof.

1. Two unique planes intersect. Which geometric term describes the intersection?

/ G.2.D / A: line

1. Look at the diagram.

Determine the values for a andb that would make the quadrilateral a parallelogram. / G.3.F / C: a = 13.5, b = 106

1. Look at the triangle.

Determine the length of y. Express your answer in simplified radical form. / G.3.D /

1. Lines l, m, and n lie in the same plane. Line m is perpendicular to line l. Line n is perpendicular to line l.

Which statement is true? / G.2.A / B: Line m and line n are parallel.

1. While walking around Seattle, Mary climbed several steep streets. One of the steepest streets, Roy Street, has a slope angle of 11.9° according to the tour guide. After walking 100 feet up the hill, she wanted to determine how high she had climbed.

Use a trigonometric ratio (sine, cosine, tangent) to determine how high Mary climbed.
Be sure to write the equation and show the steps you used to solve the equation. Round your answer to the nearest foot. / G.3.E /

Rounded to nearest foot: 21 ft

1. Determine how many miles a person will run during a 5-kilometer race. Write your answer on the line.

1 km ≈ 0.62 mi / G.6.F / ≈3.1 miles

1. Which statement is an example of inductive reasoning?

/ G.1.A / B: Squares have equal sides. This figure has equal sides, therefore this figure is a square.

1. The rhombus QRST is made of two congruent triangles. Given mQRS = 34° determine the measure of S.

/ G.3.F/G.3.G / C: 146°

1. Determine whether the conjecture is true or false. Give a counterexample for a false conjecture.

Given: points A, B, C, and D
Conjecture: A, B, C, and D are coplanar / G.1.E / False. Any three points define a plane. Points A, B, and C define a unique plane. Point D does not have to be on this plane.

1. Identify the congruent triangles in the diagram and write a congruence statement.

/ G.3.B / B: Δ LSK Δ MSN

1. Determine cosI in ΔGHI.

/ G.3.E / D:

1. Write the contrapositive of the conditional statement. Determine if the contrapositive is true or false. If it is false, find a counterexample.

“Two angles measuring 180 degrees are supplementary” / G.1.D / C: Non-supplementary angles and not two angles measuring 180 degrees. True

1. Complete this chart.

/ G.3.J / Triangular Prism:
Edges:9, faces:5, vertices: 6
Square Pyramid:
Edges: 8, faces:5, vertices: 5
Cube:
Edges:12, faces:6, vertices:8
Hexagonal Pyramid:
Edges:12, faces:7, vertices:7
Hexagonal Prism:
Edges:18, faces:8, vertices:12

1. Determine which statement is a property of all rectangles.

/ G.3.G / D: Four right angles.

1. The figure is a rectangular prism with dimensions 12 inches long, 5 inches wide and 7 inches tall. Determine the length of .

Write your answer on the line. / G.3.D / BI=
BI≈14.76 inches

1. Given B(–4, –6), determine which reflection would result in B’(6, 4).

/ G.5.A / C: Reflected over the line y = –x.

1. Determine the exact length of x in ΔHJK.

/ G.3.C / C: 10

1. If you are going 50 miles per hour, determine how many feet per second you are traveling.

/ G.6.F /

1. The ratio of a pair of corresponding sides in two similar triangles is 5:3. The area of the smaller triangle is 108 in2. What is the area of the larger triangle?

/ G.6.D /

1. Jessie is working on the roof of her house. She has measured the angle of the roof and the length of the roof. Determine the width of the house, w.

/ G.3.E /

1. The segment bisector is the midpoint.

/ G.1.D / Inverse: The non-segment bisector is not the midpoint
True

1. ΔRST has vertices R(3, 3), S(6, –2), and T(0, –2). Classify ΔRST based on its sides.

/ G.4.C / A: isosceles

1. Look at the given information for quadrilateral ABCD.

is not parallel to

• Draw and label a shape that satisfies all of the given information.
• Determine the most specific name for the shape.

/ G.7.E/G.3.G /
»

»
Isosceles Trapezoid

1. Martina has a calculator box that has a volume of 29 cubic inches.

1 inch = 2.54 centimeters
Determine the volume of the calculator box to the nearest cubic centimeter. / G.6.F /

1. Determine the image of Y(–4, 7) under the translation of :

(x, y)  (x + 3, y – 5). / G.5.B / A: Y(–1, 2)

1. Look at the figure.

What additional information do you need to show the triangles below are similar using the Side-Angle-Side Similarity Theorem? / G.3.B / A: FH = 12

1. Find sin C as a decimal rounded to the nearest hundredth.

/ G.3.E / D: 0.87

1. Two similar figures have a ratio of volumes of 64:27. What is the ratio of similarity?

/ G.6.D / Ratio of Similarity is 4:3

1. Michael is 5 feet tall. Michael measures his shadow as 8 feet long. A tree in his backyard has a shadow that is 25 yards long. How tall is the tree?

/ G.3.B /

1. Look at the pair of triangles.

Which statement is true? / G.1.E / D: There is not enough information to determine similarity or congruence.

1. Steven built a box for his vegetable garden in the shape of a rectangular prism. The volume of the vegetable garden was 24 cubic feet. He built another garden box that was two times longer and two times higher. He thinks the volume will be twice as much. Explain why Steven is not correct.

If Steven wants his second garden box to have twice the volume, what should he do instead? / G.6.D / Steven is not correct. By doubling two dimensions, he has created a rectangular prism with 4 times the volume.
Original box volume: xyz
New box volume: (2x)(2y)(z)= 4xyz
If Steven wanted to double the volume of his garden, he would need to double only one of the dimensions (probably the length or width)

1. To the nearest degree, what is m∠G?

/ G.3.E / B: 57

1. JKLM is an isosceles trapezoid with J(0, –1), K(–2, 3) and M(6, –1). Determine the coordinates of L.

/ G.4.B / D: L (8, 3)

1. Given a║b, determine which relationship must be true.

/ G.2.B / B: 2 and 8 are supplementary.

1. Determine which triangle is similar to ΔDEF.

/ G.3.B / C:

1. Name all segments skew to .

/ G.1.F / D:

1. Determine which theorem or postulate can be used to prove that these two triangles are similar.

/ G.3.B / A: AA

1. Cody is standing 14 feet from the base of the tree. The top of the tree makes a 60 angle with the ground at the point where he is standing.

Determine the height of the tree. Round your answer to two decimal places. / G.3.C /

1. Given a║b

m3 = 5x + 10 and
m5 = 3x + 10, determine the value of x. / G.2.B / C: 20

1. In circle C, m= 72. Determine mBCD.

Write your answer on the line. / G.3.H / mBCD=108˚

1. Determine which set of measures could represent the sides of a right triangle.

/ G.3.D / D: 9, 12, 15

1. Determine the exact value of x in ΔLMN.

/ G.3.C / C:

1. ΔRST has vertices R(3, 3), S(6, –2), and T(0, –2). Classify ΔRST based on its sides.

/ G.4.C / A: isosceles

1. In the diagram:

Given:

Prove: / G.3.B / Statement / Justification
/ Given
/ Given
/ Vertical angles are congruent
∆DBA≅∆CBE / AAS congruency

1. Determine the value of y.

/ G.3.H / D: 4.5

1. For rhombus GHJK, determine m1.

/ G.3.G / C: 90°

1. Given quadrilateral XYWZ, determine whether and are parallel, perpendicular or neither.

W(0, –3), X(–1, 5), Y( 2, 5) Z(–1, 2) / G.4.C /

Neither

1. Determine the value of x and y so that QRST will be a parallelogram.

/ G.3.F/G.3.G / A: x = 6, y = 42

1. Two angles measuring 90° are complementary.

/ G.1.D / Inverse: Two angles whose sum is not 90˚ are not complementary
True

1. Which statement is an example of deductive reasoning?

/ G.1.A / B: Dogs are mammals. Mammals breathe oxygen. Therefore dogs breathe oxygen.
If and ║, determine which theorem or postulate can be used to prove . / G.3.B / C: SAS

1. Identify which of the following is a property of a parallelogram.

/ G.3.F / D: The diagonals bisect each other.