Question
Question 1
(Multiple Choice Worth 1 Points)
(02.03 MC)
What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?
Triangle ABC is drawn with a single hash mark between A and B and triangle DEF is marked with a single hash mark between D and E. Angle B and angle E are marked congruent.
segment AC≅segment EF
segment BC≅segment FE
segment AC≅segment FE
segment BC≅segment EF
Question 2
(Multiple Choice Worth 1 Points)
(02.03 LC)
If ΔABC ≅ ΔFDE, which of the following statements is true?
∠A ≅ ∠F
∠B ≅ ∠F
∠A ≅ ∠D
∠B ≅ ∠E
Question 3
(Multiple Choice Worth 1 Points)
(02.03 MC)
Are triangles ADC and EBC congruent?
triangle ADC is overlapping triangle EBC so that they both share angle ACE, point B is on segment AC, point D is on segment EC, segments AD and EB intersect at point F, segments BC and DC are each marked with one dash, and angles CAD and CEB are each marked with an arc
Yes, by SSS
Yes, by AAS
Yes, by SAS
Not enough information
Question 4
(Multiple Choice Worth 1 Points)
(02.03 LC)
The grid shows Figure Q and its image Figure Q′ after a transformation.
Figure Q is a pentagon drawn on a coordinate grid with vertices in clockwise order at point 2 comma 4, point 3 comma 7, point 7 comma 5, point 5 comma 4, and point 4 comma 2. Figure Q’ is a pentagon drawn with vertices in clockwise order at point negative 2 comma 4, point negative 4 comma 2, point negative 7 comma 3, point negative 5 comma negative 7, and point negative 4 comma 5.
Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?
Clockwise rotation of 180° about the origin
Counterclockwise rotation of 90° about the origin
Clockwise rotation of 90° about the origin
Counterclockwise rotation of 270° about the origin
Question 5
(Multiple Choice Worth 1 Points)
(02.03 MC)
If ΔABC ≅ ΔEDF where the coordinates of A(0, 2), B(2, 4), and C(2, −1), what is the measure of DF?
3
3.1
5
5.9
Question 6
(Multiple Choice Worth 1 Points)
(02.03 MC)
Andrew draws triangle ABC. He then constructs a perpendicular bisector from vertex A that intersects side BC at point D. What can Andrew conclude, based on his drawing?
AB = BC
BD = DC
AD = BC
AC = BC
Question 7
(Multiple Choice Worth 1 Points)
(02.03 MC)
What coordinate for F would make triangle ABC and triangle DEF congruent?
Triangle ABC is shown. For triangle ABC, A is at 1, 0, B is at negative 1, 2, C is at 2, 3. Two other coordinates are shown. D is at negative 1, 0, E is at 1, 2.
(−2, 4)
(−2, 3)
(−3, 3)
(−3, 4)
Question 8
(Multiple Choice Worth 1 Points)
(02.03 MC)
If a rotation takes triangle CAT to C′A′T′, what is C′T′?
triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units
3
square root of 17
5
Cannot be determined
Question 9
(Multiple Choice Worth 1 Points)
(02.03 LC)
If ΔFGH ≅ ΔIJK, which segment is congruent to segment GH?
segment HF
segment JK
segment IJ
segment FG
Question 10
(Multiple Choice Worth 1 Points)
(02.03 MC)
Eden is cutting two triangular tiles for her bathroom. She needs the tiles to be congruent but is not sure she is cutting them that way. Eden has ensured that one side of both tiles is congruent. Which pair of sides would Eden need to compare in order to make sure the triangles are congruent by HL?
triangle ABC with coordinates A at 1 comma 4, B at 2 comma 4, C at 1 comma 1, and a right angle symbol at A and length of AB of 1 unit, triangle EFD with coordinates E at 2 comma negative 2, F at one comma negative 2, D at 2 comma 1 and a right angle symbol at E with length of EF of 1 unit
segment ACandsegment ED
segment ACandsegment FD
segment BCandsegment EF
segment BCandsegment FD
(Multiple Choice Worth 1 Points)
(02.03 MC)
What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?
Triangle ABC is drawn with a single hash mark between A and B and triangle DEF is marked with a single hash mark between D and E. Angle B and angle E are marked congruent.
segment AC≅segment EF
segment BC≅segment FE
segment AC≅segment FE
segment BC≅segment EF
Question 2
(Multiple Choice Worth 1 Points)
(02.03 LC)
If ΔABC ≅ ΔFDE, which of the following statements is true?
∠A ≅ ∠F
∠B ≅ ∠F
∠A ≅ ∠D
∠B ≅ ∠E
Question 3
(Multiple Choice Worth 1 Points)
(02.03 MC)
Are triangles ADC and EBC congruent?
triangle ADC is overlapping triangle EBC so that they both share angle ACE, point B is on segment AC, point D is on segment EC, segments AD and EB intersect at point F, segments BC and DC are each marked with one dash, and angles CAD and CEB are each marked with an arc
Yes, by SSS
Yes, by AAS
Yes, by SAS
Not enough information
Question 4
(Multiple Choice Worth 1 Points)
(02.03 LC)
The grid shows Figure Q and its image Figure Q′ after a transformation.
Figure Q is a pentagon drawn on a coordinate grid with vertices in clockwise order at point 2 comma 4, point 3 comma 7, point 7 comma 5, point 5 comma 4, and point 4 comma 2. Figure Q’ is a pentagon drawn with vertices in clockwise order at point negative 2 comma 4, point negative 4 comma 2, point negative 7 comma 3, point negative 5 comma negative 7, and point negative 4 comma 5.
Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent?
Clockwise rotation of 180° about the origin
Counterclockwise rotation of 90° about the origin
Clockwise rotation of 90° about the origin
Counterclockwise rotation of 270° about the origin
Question 5
(Multiple Choice Worth 1 Points)
(02.03 MC)
If ΔABC ≅ ΔEDF where the coordinates of A(0, 2), B(2, 4), and C(2, −1), what is the measure of DF?
3
3.1
5
5.9
Question 6
(Multiple Choice Worth 1 Points)
(02.03 MC)
Andrew draws triangle ABC. He then constructs a perpendicular bisector from vertex A that intersects side BC at point D. What can Andrew conclude, based on his drawing?
AB = BC
BD = DC
AD = BC
AC = BC
Question 7
(Multiple Choice Worth 1 Points)
(02.03 MC)
What coordinate for F would make triangle ABC and triangle DEF congruent?
Triangle ABC is shown. For triangle ABC, A is at 1, 0, B is at negative 1, 2, C is at 2, 3. Two other coordinates are shown. D is at negative 1, 0, E is at 1, 2.
(−2, 4)
(−2, 3)
(−3, 3)
(−3, 4)
Question 8
(Multiple Choice Worth 1 Points)
(02.03 MC)
If a rotation takes triangle CAT to C′A′T′, what is C′T′?
triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units
3
square root of 17
5
Cannot be determined
Question 9
(Multiple Choice Worth 1 Points)
(02.03 LC)
If ΔFGH ≅ ΔIJK, which segment is congruent to segment GH?
segment HF
segment JK
segment IJ
segment FG
Question 10
(Multiple Choice Worth 1 Points)
(02.03 MC)
Eden is cutting two triangular tiles for her bathroom. She needs the tiles to be congruent but is not sure she is cutting them that way. Eden has ensured that one side of both tiles is congruent. Which pair of sides would Eden need to compare in order to make sure the triangles are congruent by HL?
triangle ABC with coordinates A at 1 comma 4, B at 2 comma 4, C at 1 comma 1, and a right angle symbol at A and length of AB of 1 unit, triangle EFD with coordinates E at 2 comma negative 2, F at one comma negative 2, D at 2 comma 1 and a right angle symbol at E with length of EF of 1 unit
segment ACandsegment ED
segment ACandsegment FD
segment BCandsegment EF
segment BCandsegment FD
Answers
GPT-4o mini
Here are the answers for each of the questions:
**Question 1:**
- **Answer:** segment BC ≅ segment EF
**Question 2:**
- **Answer:** ∠A ≅ ∠F
**Question 3:**
- **Answer:** Yes, by AAS
**Question 4:**
- **Answer:** Clockwise rotation of 180° about the origin
**Question 5:**
- **Answer:** 5
**Question 6:**
- **Answer:** BD = DC
**Question 7:**
- **Answer:** (−3, 3)
**Question 8:**
- **Answer:** Cannot be determined
**Question 9:**
- **Answer:** segment IJ
**Question 10:**
- **Answer:** segment AC and segment ED
These answers should help you with your understanding of triangle congruences and transformations!
**Question 1:**
- **Answer:** segment BC ≅ segment EF
**Question 2:**
- **Answer:** ∠A ≅ ∠F
**Question 3:**
- **Answer:** Yes, by AAS
**Question 4:**
- **Answer:** Clockwise rotation of 180° about the origin
**Question 5:**
- **Answer:** 5
**Question 6:**
- **Answer:** BD = DC
**Question 7:**
- **Answer:** (−3, 3)
**Question 8:**
- **Answer:** Cannot be determined
**Question 9:**
- **Answer:** segment IJ
**Question 10:**
- **Answer:** segment AC and segment ED
These answers should help you with your understanding of triangle congruences and transformations!