Question 1

Question

A)Consider right triangles ΔABC and ΔXYZ. Angle B and angle Y are congruent. The hypotenuse of each triangle is AC¯¯¯¯¯¯¯¯ and XZ¯¯¯¯¯¯¯¯, and they are congruent. What other corresponding parts must be congruent to show that ΔABC≅ΔXYZ by the HL Congruence Theorem?(1 point)
Responses

BC¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper X upper Z with bar

AB¯¯¯¯¯¯¯¯≅YZ¯¯¯¯¯¯¯
Modifying above upper A upper B with bar congruent to Modifying above upper Y upper Z with bar

BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper X upper Y with bar

AB¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper A upper B with bar congruent to Modifying above upper X upper Y with bar
Question 2
A)Malik is comparing 2 right triangles. Both triangles have a hypotenuse of 13 units. The first triangle has a leg of 12 units and the other triangle has a leg of 5 units. How could Malik prove that the two triangles are congruent?(1 point)
Responses

He can conclude that they are congruent because they are both right triangles.
He can conclude that they are congruent because they are both right triangles.

He could apply the concept of HL and show that the two triangles are congruent.
He could apply the concept of HL and show that the two triangles are congruent.

He would need additional information to prove that the two triangles are congruent.
He would need additional information to prove that the two triangles are congruent.

He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent.
He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent.
Question 3
A)
Use the image to answer the question.

Four points upper A, upper B, upper C, and upper D form the corners of a rectangle plotted on a 4 rows by 5 columns grid.

Ignacio wants to prove that ΔABC≅ΔDCB. He says that he knows AC¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ because diagonals in rectangles are congruent. What rule can he use to prove that BC¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯?

(1 point)
Responses

the Reflexive Property
the Reflexive Property

the HL Theorem
the HL Theorem

the Pythagorean Theorem
the Pythagorean Theorem

the Distributive Property
the Distributive Property
Question 4
A)
Use the image to answer the question.

Five points upper A, upper B, upper C, upper D, and upper E form two right triangles from two intersecting lines.

If C is the midpoint of AB¯¯¯¯¯¯¯¯ and DE¯¯¯¯¯¯¯¯, what is the length of AB¯¯¯¯¯¯¯¯?

(1 point)
Responses

26
26

24
24

17
17

13
13
Question 5
A)
Use the image to answer the question.

Four points upper A, upper B, upper C, and upper D are plotted and joined by line segments, including two diagonal intersecting lines, to form three triangles.

In the diagram above, △ABC ≅△BAD
. If AC=8 m and AB=17 m, how long is AD¯¯¯¯¯¯¯¯?

(1 point)
Responses

20 m
20 m

17 m
17 m

19 m

Answer 1

Sure! Here are the answers to your questions based on the information provided:

Question 1: To show that ΔABC ≅ ΔXYZ by the HL Congruence Theorem, since angle B and angle Y are congruent and the hypotenuses AC and XZ are congruent, we need the legs of the triangles to be congruent:

• Response: BC¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯ (this is correct to use as the third corresponding side that implies HL).

Question 2: Malik has two right triangles with hypotenuses of 13 units but different legs. He would need to check if the triangles meet the criteria for the HL Theorem:

• Response: He could apply the concept of HL and show that the two triangles are congruent.

Question 3: To prove that BC¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ (the segment BC in both triangles), Ignacio can use the property that a segment is equal to itself:

• Response: the Reflexive Property.

Question 4: If C is the midpoint of AB¯¯¯¯¯¯¯ and DE¯¯¯¯¯¯¯¯, the question about the length of AB depends on the given lengths but normally involves using information from the midpoint:

• Response: 26 (assuming this value fits the context of the problem, as C is a midpoint).

Question 5: If △ABC ≅ △BAD and you've been given AC and AB, you could also infer the length of AD based on corresponding parts:

• Response: 17 m (if AD corresponds to AB in the congruency context).

If you have any additional or specific clarifications on the images or context, I can further assist!