Geometry

<object:standard:ma.912.g.3.3>Two quadrilaterals EFGH and IJKL are drawn on a coordinate grid. The coordinates of the vertices of each quadrilateral are given below.

EFGH – E (1, 4), F (2, 4), G (2, 2), H (1, 2)

IJKL – I (-4, -1), J (-1, -1), K(-1, -7), L(-4, -7)

Which statement about the two quadrilaterals is true?

[removed] The side lengths of IJKL are three times the corresponding side lengths of EFGH.

[removed] The side lengths of IJKL are congruent to the corresponding side lengths of EFGH.

[removed] The side lengths of IJKL are not proportional to the corresponding side lengths of EFGH.

[removed] The side lengths of IJKL are half of the corresponding side lengths of EFGH.

Question 2 (Multiple Choice Worth 4 points)

(3.03 MC) <object:standard:ma.912.g.4.3>

The figure below shows two triangles that were constructed using a compass and straightedge. Justin used the ASA postulate to prove that triangle XYZ is congruent to triangle ABC.

Two congruent obtuse scalene triangles, XYZ and ABC.

As part of the proof Justin showed that side YZ is congruent to side BC. Using this congruency, which of these other steps would Justin have likely performed to prove that the two triangles are congruent by the ASA postulate?

[removed] Place the compass on Y and draw an arc that passes through X.

[removed] Place the compass on X and draw an arc to cross side XY at L and side ZX at M . Place the compass on L and set the width of the compass to segment LM.

[removed] Place the compass on X and set the width to side XZ. Place the compass on A and draw an arc to cross side AC at point C.

[removed] Place the compass on Z and draw an arc to cross side YZ at L and side ZX at M. Place the compass on L and set the width of the compass to segment LM.

Question 3 (Multiple Choice Worth 4 points)

(4.04 MC) <object:standard:ma.912.g.5.3>

The picture shows a portion of an irrigation system for a farm. LM is the main water pipe.

Triangle KML has the measure of angle MKL equal to 90 degrees, angle KLM equal to 60 degrees, and length of KM equal to 11 feet

What is the length of the main water pipe LM?

[removed] 19.1 feet

[removed] 12.7 feet

[removed] 5.5 feet

[removed] 6.4 feet

Question 4 (Multiple Choice Worth 4 points)

(3.01 MC) <object:standard:ma.912.g.4.7>

Nancy cuts a piece of cardboard in the shape of a triangle. What could be the lengths of the three sides of the triangle?

[removed] 2 cm, 4 cm, 7 cm

[removed] 2 cm, 3cm, 4cm

[removed] 2 cm, 3cm, 6cm

[removed] 2 cm, 4 cm, 1 cm

Question 5 (Multiple Choice Worth 4 points)

(4.01 – 4.04 MC) <object:standard:ma.912.g.5.4>

The figure shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced.

Triangle ABC has length of BC equal to 10 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees and measure of angle DCB is 30 degrees.

What is the length of the wood that is needed to replace AD?

[removed] 4.2 inches

[removed] 5.7 inches

[removed] 2.5 inches

[removed] 1.3 inches