DISTRICT_Geo_S1_Module2_EOM_Pt1

A video game company is designing a game based on professional race cars. Professional race cars have a length of 570 cm and a width of 180 cm. The company wants a scaled image of the race car to fit within a rectangle on the game screen with a length of 13 cm and a width of 4 cm.

A. Knowing that the maximum width of the rectangle is 4 cm, what scale factor would result in the largest possible race car width that fits in the rectangle?

B. The video game company wants the width of the car on the game screen to be no smaller than 3 cm.  What scale factor would result in the smallest possible image of the race car that meets this additional specification?

Tags

G.MG.3

A dilation from the origin by scale factor r = 1/2 maps quadrilateral ABCD to quadrilateral A′B′C′D′ (not shown).

What are the vertices of quadrilateral A′B′C′D′ (in order)?

Tags

G.SRT.1

G.SRT.2

What is true about these quadrilaterals?  Select your answers from the drop-down lists.

Quadrilateral ABCD is ​ (a)   to quadrilateral A'B'C'D', and ∠ABC is ​ (b)   to ∠A'B'C'

• similar
• congruent

Tags

G.SRT.1

G.SRT.2

Consider the four segments. The center of dilation O is not shown.

Select options from the drop-down lists to create true statements.

A dilation of segment CD from center O with scale factor r, where 0 < r < 1, creates a figure that could be ​ (a)  

A dilation of segment CD from center O with scale factor r, where r > 1, creates a figure that could be ​ (b)  

A dilation of segment CD from center O with scale factor r, where r = 1, creates a figure that could be ​ (c)  

• segment AB
• segment EF
• segment GH

Tags

G.SRT.1

If Figure 1 is similar to Figure 2, which of the following must be true?

• All corresponding lengths are equal.

• All corresponding lengths are in equal ratio.

• All corresponding angle measures are equal.

• There exists a finite composition of rigid motions that maps Figure 1 to Figure 2.

• • There exists a finite composition of dilations and rigid motions that maps Figure 1 to Figure 2.

Tags

G.SRT.2

In the diagram, BD ⊥ AC and AE ⊥ CB. Complete the proof to show △AEC∼△BDC.

∠BDC and ∠AEC are right angles by the definition of ​ (a)   and all right angles are congruent,

so ∠BDC ≅ ∠AEC.  Both △AEC and △BDC share ∠C, and ∠C ≅ ∠C by the ​ (b)   . Therefore, △AEC ∼ △BDC by the ​ (c)   criterion for proving similar triangles.

• perpendicular lines
• reflexive property
• AA
• parallel lines
• vertical angles
• transitive property
• substitution property
• SAS

Tags

G.SRT.3

Eva is trying to determine the height of a tree.  When she looks up from the ground 59 m away from a shorter tree, the top of the shorter tree and taller tree line up. If the shorter tree is 38 m tall and Eva is 131 m from the taller tree, how tall is the taller tree?  Round your answer to the nearest hundredth.

• 203.39 m

• 84.37 m

• 46.37 m

• 17.11 m

Tags

G.MG.1