Question

Two triangles are shown to be congruent by identifying a combination of translations, rotations, or reflections that move one figure onto the other. If ΔMOP ≅ ΔCUP, which angle must be congruent to ∠CPU? Why?

Answer 1

∠MPO because corresponding parts of congruent triangles are congruent.

Explanation:

The definition of congruent triangles says the corresponding parts of congruent triangles are congruent (CPCTC).

Since ΔMOP ≅ ΔCUP, ∠CPU corresponds to ∠MPO.

Answer 2

In the given question,

Δ MOP ≅ Δ CUP

so, ∠MPO ≅ ∠CPU

Explanation:

As when we write Δ ABC ≅ Δ DEF ------------(1)

it means that the points are taken in such an order that the congruent sides and angles can be easily found from the notation, i.e., if we take sides and angles from the notation of RHS in the same order as those taken from the notation in LHS, then the corresponding sides and angles will be congruent.

e.g., from (1)

∠ACB ≅ ∠DFE

but, ∠ ABC is not congruent to ∠ EDF

and,

AB ≅ DE but, AC is not congruent to EF.

Now, in the given question,

Δ MOP ≅ Δ CUP

so, ∠MPO ≅ ∠CPU