Question 1(Multiple Choice Worth 1 points)

Question

(02.03 MC)

If ΔABC ≅ ΔEDF where the coordinates of A(−1, 1), B(2, 4), and C(3, 1), what is the measure of EF?

3
3.2
4
4.6
Question 2(Multiple Choice Worth 1 points)
(02.03 MC)

Are triangles ABC and DEC congruent?

triangle ABC and DEC intersect at point C, segments BC and EC are each marked with one dash, and angles A and D are each marked with an arc

Yes, by SSS
Yes, by AAS
Yes, by SAS
Not enough information
Question 3(Multiple Choice Worth 1 points)
(02.03 MC)

Declan draws triangle WXY. He then constructs a perpendicular bisector from vertex W that intersects side XY at point Z. What can Declan conclude, based on his drawing?

WX = XY
WZ = YX
WY = XY
YZ = XZ
Question 4(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 5(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 AC of 3 units, 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 ED of 3 units

segment AC and segment EF
segment AC and segment FD
segment BC and segment EF
segment BC and segment FD
Question 6(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 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 0, 3, 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, negative 2.

(−3, −3)
(−3, −2)
(−2, −3)
(−2, −2)
Question 8(Multiple Choice Worth 1 points)
(02.03 LC)

If ΔABC ≅ ΔFDE, which of the following statements is true?

∠A ≅ ∠E
∠B ≅ ∠F
∠C ≅ ∠E
∠A ≅ ∠D
Question 9(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 10(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

Answer 1

Here are the answers to each question provided in the format you requested:

Question 1

To find the measure of EF in ΔABC ≅ ΔEDF, we can calculate the lengths of sides AB, BC, and CA using the given coordinates:

• A(-1, 1) to B(2, 4): \[ AB = \sqrt{(2 - (-1))^2 + (4 - 1)^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2} \]
• B(2, 4) to C(3, 1): \[ BC = \sqrt{(3 - 2)^2 + (1 - 4)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{10} \]
• C(3, 1) to A(-1, 1): \[ CA = \sqrt{(-1 - 3)^2 + (1 - 1)^2} = \sqrt{(-4)^2} = 4 \]

Since the triangles are congruent, the length of EF (the side corresponding to AC) is 4.

Answer: 4

Question 2

Since triangle ABC and triangle DEC share angle C and corresponding sides BC and EC are marked congruent, the triangles are congruent by the SAS (Side-Angle-Side) postulate.

Answer: Yes, by SAS

Question 3

Declan's construction of a perpendicular bisector from vertex W to side XY at point Z means that WZ is equal to the length from W to the line XY, but it does not provide relationship between the other sides. However, based on the properties of perpendicular bisectors, the conclusion is:

\[ YZ = XZ \]

Answer: YZ = XZ

Question 4

To prove triangles ABC and DEF are congruent by SAS, we need one additional piece of information about the sides:

Since angles B and E are marked congruent and the included side AB is given equal to DE, we can use segment AC to complete the proof.

Answer: segment AC ≅ segment EF

Question 5

For the triangles to be congruent by HL (Hypotenuse-Leg), we must compare the hypotenuse and one leg. Given that both triangles have been given congruent legs of length 3, the pair needed to compare the hypotenuse is:

Answer: segment AC and segment EF

Question 6

For triangles Q and Q' to be congruent through a transformation, we look for a possible 180° rotation about the origin since all points would be reflected appropriately:

Answer: Clockwise rotation of 180° about the origin

Question 7

To find the coordinate for F that makes triangles ABC and DEF congruent, we look for a coordinate that matches the distances and configurations of triangle ABC. To find the correct point for F, we need to match the angles and resulting sides. The potential coordinates are:

• A(0, 3), B(-1, 2), C(2, 3) calculated against D(-1, 0) and E(1, -2), testing points leads to geometric congruence involving side lengths.

After calculating through options: Answer: (−2, −2)

Question 8

If triangles are congruent (ΔABC ≅ ΔFDE), by definition of congruence:

Answer: ∠A ≅ ∠E

Question 9

If triangle CAT rotates to C'A'T', the corresponding sides remain congruent. Specifically, C'T' cannot derive from vague rotations without side lengths, leading to indeterminate aspects in an abstract form.

Answer: Cannot be determined

Question 10

In congruent triangles ΔFGH and ΔIJK, corresponding segments stay equal in measure, meaning:

Answer: segment IJ

This gives a clear set of answers based on geometric theories and principles.