Question

Suppose ΔXYZ is given, and you want to construct ΔABC so that the triangles are congruent. Which constructions would guarantee that ΔXYZ ≅ ΔABC?
Check all that apply.

A:constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX
B:constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and ∠C ≅ ∠Z
C:constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X
D:constructing ΔABC so that CA ≅ ZX, ∠B ≅ ∠Y, and ∠C ≅ ∠Z
E:constructing ΔABC so that ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z

Answer 1

Answer:

A,C,D is the correct answer

Step-by-step explanation:

Suppose ΔXYZ is given, and you want to construct ΔABC so that the triangles are congruent. Which constructions would guarantee that ΔXYZ ≅ ΔABC? Check all that apply.

constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX

constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and ∠C ≅ ∠Z

constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X

constructing ΔABC so that CA ≅ ZX, ∠B ≅ ∠Y, and ∠C ≅ ∠Z

constructing ΔABC so that ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z

Answer 2

Answer:

A: constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX

C: constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X

Step-by-step explanation:

* Lets revise the ways of constructing a triangle

- There are 3 ways to construct a triangle

# You must have length of one side and measures of two angles which

  are the endpoint of the side

# You must have a length of two sides and the measure of the including

  angle between the two sides

# You must have the length of the 3 sides

* Lets solve the problem

∵ Δ XYZ ≅ Δ ABC

∴ XY = AB , YZ = BC , ZX = CA

∴ m∠ X = m∠ A , m∠ Y = m∠ B , m∠ Z = m∠ C

- To construct Δ ABC You can use:

# The length of the 3 sides

∵ AB ≅ XY , BC ≅ YZ , CA ≅ ZX

∴ constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX ⇒ A

# The length of two sides and the measure of the including angle

∵ AB ≅ XY , CA = ZX

∵ The including angles between the sides are ∠A and ∠X

∴ constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X ⇒ C

# The length of one side and the measures of two angles which are

   the endpoints of the side

∵ CA ≅ ZX

∵ The end points are C , A and Z , X

∴ constructing ΔABC so that CA ≅ ZX, ∠A ≅ ∠X, and ∠C ≅ ∠Z

- But this answer not in the choices

∴ The answer is A and C