Answers SSHS Geometry Sem 1 IMA 301Directed Line Segments and Modeling

Directed Line Segments and Modeling — Unit test Answers

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Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

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3 ft

4 ft

18 ft

12 ft

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

∠DFE is 4 times greater than ∠GFH.

∠FHG is the measure of ∠FED.

∠DFE is congruent to ∠GFH.

∠FHG is congruent to ∠EFD.

Triangle ABC was dilated using the rule .

10 units

12 units

16 units

20 units

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

0.1

Option

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

LO ≅ LM

OA ≅ MA

LOA ≅ LMA

LAO ≅ LAM

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.

Triangles J K L and M N R are shown.

KL ≅ NR

∠L ≅ ∠R

∠K ≅ ∠N

JK ≅ MN

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

∠DFE is 4 times greater than ∠GFH.

∠FHG is the measure of ∠FED.

∠DFE is congruent to ∠GFH.

∠FHG is congruent to ∠EFD.

If point P is of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

4:1

4:3

4:7

4:10

Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

Consider the two triangles.

Option

On a coordinate plane, a line is drawn from point A to point B. Point A is at (9, negative 8) and point B is at (negative 6, 7).

(2, –1)

(4, –3)

(–1, 2)

(3, –2)

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Yes, if JL ≅ XZ.

Yes, if XZ = 10.

No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

No, because the leg of one triangle is equal in length to the leg of the other triangle.

On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units.

Yes, because corresponding sides are parallel and have lengths in the ratio

Yes, because both figures are rectangles and all rectangles are similar.

No, because the center of dilation is not at (0, 0).

No, because corresponding sides have different slopes.

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

the reflexive property

ASA

AAS

the third angle theorem

Which pair of triangles can be proven congruent by SAS?

2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.

2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.

2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.

2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.