AnswersMathematics ITriangle Congruence

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To solve the problem using these steps, what are the dimensions of the rectangle she should draw? Expand Image

A
2 units by 4 units
B
3 units by 4 units
C
4 units by 5 units
D
3 units by 5 units
2
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What is the area of triangle RST ?

A
6 square units
B
12 square units
C
18 square units
D
9 square units
3

First, translate ____________________. Next, rotate triangle ABC about cap b to align the sides and angles.

A
vertex cap A to vertex cap z
B
vertex cap b to vertex cap z
C
vertex cap b to vertex cap y
D
vertex cap A to vertex cap y
4

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

A
angle cap f cap h cap g is congruent to angle cap j cap k cap g because right angles are congruent.
B
angle cap f cap g cap h is congruent to angle cap k cap g cap j because vertical angles are congruent.
C
angle cap j cap k cap g is congruent to angle cap h cap f cap g because vertical angles are congruent.
D
angle cap h cap f cap g is congruent to angle cap k cap j cap g because alternate interior angles are congruent.
5

Could triangle ABC be congruent to triangle ADC by SSS? Explain.

A
Yes, but only if line segment BC is congruent to line segment DC .
B
No, because line segment AB is congruent to line segment DA .
C
Yes, but only if line segment AB is congruent to line segment DC .
D
No, because line segment AB is not congruent to line segment AC .
6

Which best explains whether or not triangles RST and ACB are congruent?

A
The figures are not congruent. Point cap r corresponds to point cap A , but cap s corresponds to cap b and cap t corresponds to cap c .
B
The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the y -axis and a translation 2 units down.
C
The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the x -axis and a translation 2 units to the left.
D
The figures are not congruent. Point cap r does not correspond with point cap A .
7

Triangle RST is rotated 180 degrees about the origin, and then translated up 3 units. Which congruency statement describes the figures?

A
triangle RST is congruent to triangle ABC
B
triangle RST is congruent to triangle BAC
C
triangle RST is congruent to triangle ACB
D
triangle RST is congruent to triangle BCA
8

What is the perimeter of kite KLMN ?

A
2 square root of 2 plus 2 square root of 5 units
B
4 square root of 5 units
C
square root of 14 units
D
square root of 2 plus square root of 5 units
9

Which pair of triangles can be proven congruent by the HL theorem?

A
Image with description 2 triangles have one congruent angle and 2 congruent sides.
B
Image with description 2 right triangles have congruent hypotenuses.
C
Image with description 2 right triangles have congruent hypotenuses and another congruent side.
D
Image with description 2 triangles have 3 congruent sides.
10

Which statement proves that PQRS is a parallelogram?

A
The slopes of line segment RS and line segment QP are both 3 and SP is equal to RQ is equal to square root of 45 .
B
The midpoint of line segment SQ is open paren 4 comma 5 and 1 half close paren and SQ is equal to 5 .
C
The midpoint of line segment RP is open paren 4 comma 5 and 1 half close paren and the slope of line segment RP is negative 9 halves .
D
The slopes of line segment SP and line segment RQ are both negative 2 and SP is equal to RQ is equal to square root of 45 .
11

Which rigid transformation would map triangle ABC to triangle ABF ?

A
a rotation about point cap b
B
a rotation about point cap A
C
a reflection across the line containing line segment BA
D
a reflection across the line containing line segment CB
12

Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof? Given: angle cap b is congruent to angle cap n ; line segment cap b cap c is congruent to line segment cap n cap m ; angle cap c is right; angle cap m is right Prove: triangle cap A cap b cap c is congruent to triangle cap q cap n cap m

A
line segment cap A cap b is congruent to line segment cap q cap n because they are both opposite a right angle.
B
line segment cap b cap c is congruent to line segment cap n cap m because it is given.
C
angle cap c is congruent to angle cap m because right angles are congruent.
D
angle cap A is congruent to angle cap q because of the third angle theorem.

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