Honors Geometry - 2nd 6W Exam

Refer to this diagram for the next five statements (Questions 1–5). Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

Given: ∠MRS ≅ ∠MRO

m∠MRO + m∠MRS = m∠SRO

Refer to this diagram for the next five statements (Questions 1–5). Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

Given: ∠MRS ≅ ∠MRO

m∠MRO + m∠MRS = m∠SRO

The postulate that justifies the statement is the Angle Addition Postulate.

Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

Given: ∠MRS ≅ ∠MRO

m∠MRO + m∠MRS = 180°

The theorem that justifies the statement is the Linear Pair Theorem

Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

Given: ∠MRS ≅ ∠MRO

m∠MRS = m∠MRO

Definition of Congruent Angles or the congruence/measurement postulate.

Which statement best applies the segment addition postulate to the figure below?

Segment SO consists of two adjacent segments, SR and RO which are not overlapping, therefore the sum of the lengths of the two smaller segments equals the length of the longer segment: SR + RO = SO.

Which statement best applies the reflexive property to the figure below?

∠MRS and ∠MRO are adjacent angles which have segment MR in common; MR¯≅MR¯  according to the reflexive property.

In this rug, given the horizontal segments are parallel and ∠1 ≅ ∠2, prove ∠3 ≅ ∠5.

 ∠1 ≅ ∠2 - Given 

∠1 ≅ ∠3 - Alternate Interior Angle Postulate

∠2 ≅ ∠5 - Alternate Interior Angle Postulate

∠3 ≅ ∠2 - Transitive Property

∠3 ≅ ∠5 - Transitive Property

Identify which of the following represents a translation. Choose the best representation and justification.

A translation is a transformation that does not change size or shape. The orientation of the figure will stay the exact same, but the location may change.

Given the translation (x, y) ⟶ (x + 3, y – 4), what is the translation that will return the coordinates of the image to the coordinates of the pre-image? Choose the best answer and justification.

(x – 3, y + 4); The image can always be returned to the pre-image by changing the signs of the original rule. 

Choose the best justification and the rule that translates ∆ANT to ∆A’N’T’.

(x – 5, y + 3); The ' symbol  indicates that ΔT'A'N' is the image of the translation. Each of the points moved 5 units to the left and 3 units upward.

Which of these best describes how the concept of a transformation can be applied to an authentic scenario and/or career?

In careers such as web design and graphic design, translations are often used to create exact duplicates of figures without distorting their size, shape, or the direction they're facing.

Choose the option that depicts a reflection of ∆ABC over the line y = x

 The figure below is rotated about the origin 90° counterclockwise. What will be the coordinates of A’?

(2, 5)

The picture below shows the pre-image of a rotation about the origin 180° clockwise. Which of the following shows the image of this transformation?

Charlotte designed a floor pattern for her new game room. She used only translations of the following tile to produce the pattern.

 Which of the images below shows only translations of the figure above?

Which of the following best describes the transformation rule (x,y)⟶(−x,y)?

Reflection across the y-axis

Consider the graph to the right.

Suppose you needed to dilate this figure on the same coordinate plane. Which of these dilations would create the largest possible image that could be graphed on the axes to the right without going over any of the edges?

D_5/4

Consider the graph to the right.

Suppose you needed to dilate this figure on the same coordinate plane. Which of these dilations would create the largest possible image that could fit on a new coordinate plane which only covered–5 < x < 5 and –5 < y < 5?

D_0.625 because on the pre-image, A(–4, 8) is the point that is farthest outside of the -5 to 5 boundary due to the y = 8 coordinate, and 5/8 is 0.625.

The dimensions of a tennis court are 27 feet by 78 feet. The dimensions of a ping pong table are 9 feet by 5 feet. Is a tennis court a dilation of a ping pong table? Explain why or why not.

• Correctly answer yes or no (4 points)

• Provide a clear and logical explanation (6 points)

No because if we compare the shorter side of both rectangles we would need to multiply 5 by 5.4 to dilate it to 27 feet. Using a scale factor of 5.4 would not work for the longer sides because 9 times 5.4 is not 78.

The dimensions of a rectangle are 8 inches by 9 inches. The rectangle is dilated by a scale factor of x, such that the area of the new rectangle is 288 inches squared. Find the value of x.

x = 2

The missing interior angle measure is ____ degrees

32

Find the side length of the equilateral triangle below.

29

Triangle LMN is an isosceles triangle with LM¯≅MN¯. Find the measures of the three interior angles.

44°, 44°, 92°

Find the measure of the exterior angle, formed by the sculpture and the ground, marked below in red.

132

Solve for x.

x = 14

Find the value of b.

56