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

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

you'll just earn points here

step-by-step explanation:

b and c

step-by-step explanation: