Question

Question 1
A)
Use the image to answer the question.

Triangle F G H is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle J K I is drawn with a dotted line and is located in quadrant 4.

Assess two figures using the definitions of transformations to determine whether the figures are similar. Is ΔFGH∼ΔIJK, and for what reason?

(1 point)
Responses

No. If point J was at (−6,6), the triangles would be similar.
No. If point upper J was at left parenthesis negative 4 comma 5 right parenthesis , the triangles would be similar.

Yes. All sides are proportional.
Yes. All sides are proportional.

Yes. All angles are congruent.
Yes. All angles are congruent.

No. If point J was at (6,−6), the triangles would be similar.
No. If point upper J was at left parenthesis 4 comma negative 5 right parenthesis , the triangles would be similar.
Question 2
A)Suppose one figure is mapped to a similar figure on the coordinate plane. The lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure. In a sequence of transformations from the preimage to the image, which type of transformation must occur?(1 point)
Responses

translation
translation

dilation
dilation

rotation
rotation

reflection
reflection
Question 3
A)If ΔPRQ has ∠P=30 and ∠R=127 and ΔFGH has ∠H=30 and ∠G=23, what criterion has been met to prove the triangles similar?(1 point)
Responses

SAS
SAS

SSS
SSS

ASA
ASA

AA
AA
Question 4
A)
Use the image to answer the question.

Triangles upper F upper G upper H and upper P upper Q upper R are plotted on a grid. Triangle upper P upper Q upper R is larger.

If ∠H and ∠P each equal 38 degrees and ∠G and ∠Q each equal 41 degrees, is △FHG∼△PRQ
?

(1 point)
Responses

no because m∠F
and m∠R
are unknown
no because m∠F
and m∠R
are unknown

no because the ratio of corresponding side lengths is unknown
no because the ratio of corresponding side lengths is unknown

yes because of the SSS Congruence Theorem
yes because of the SSS Congruence Theorem

yes because of the AA Similarity Theorem
yes because of the AA Similarity Theorem
Question 5
A)Given △LMN
and △VTU
, how might the AA Similarity Theorem be used to prove ΔLMN∼ΔVTU?(1 point)
Responses

Show ∠L≅∠V
and ∠M≅∠T
.
Show ∠L≅∠V
and ∠M≅∠T
.

Show ∡L+∡M+∡N=∡V+∡T+∡U=180°
.
Show ∡L+∡M+∡N=∡V+∡T+∡U=180°
.

Show LM¯¯¯¯¯¯¯¯¯:VT¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯:TU¯¯¯¯¯¯¯
.

Answer 1

Here are the answers based on the provided information and geometrical concepts:

**Question 1:**
- **Response:** Yes. All angles are congruent.
- Reason: For two triangles to be similar, their corresponding angles must be equal (AA criterion for similarity).

**Question 2:**
- **Response:** dilation
- Reason: A dilation transforms a figure by expanding or contracting it from a point, and in this case, the sides of the similar figure are twice the lengths of the corresponding sides of the original figure.

**Question 3:**
- **Response:** AA
- Reason: The Angle-Angle (AA) criterion for similarity states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

**Question 4:**
- **Response:** yes because of the AA Similarity Theorem
- Reason: Since two angles of triangle FHG are shown to be equal to two angles of triangle PRQ, the triangles are similar by the AA Similarity Theorem.

**Question 5:**
- **Response:** Show ∠L≅∠V and ∠M≅∠T.
- Reason: To use the AA Similarity Theorem, you only need to show that two angles of one triangle are congruent to two angles of another triangle.

Feel free to ask if you have any more questions!