Given: ab ≅ ae; bc ≅ de prove: ∠acd ≅ ∠adc complete the paragraph proof. we are given ab ≅ ae and bc ≅ de. this means abe is an isosceles triangle. base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠abe ≅ ∠aeb. we can then determine △abc ≅ △aed by . because of cpctc, segment ac is congruent to segment . triangle acd is an isosceles triangle based on the definition of isosceles triangle. therefore, based on the isosceles triangle theorem, ∠acd ≅ ∠adc.

In isosceles triangle - the base angles are congruent.

so,

   ∠ACD ≅ ∠ADC

Step-by-step explanation:

Given: AB ≅ AE, BC ≅ DE

If AB = AE

Then,

 ΔABE is a isosceles triangle.

The base angle of isosceles triangle are same.

So, ∠B = ∠E

Now in ΔABC and ΔAED

BC ≅ DE , ∠B = ∠E, AB ≅ AE

From side angle side theorem

ΔABC ≅ ΔAED

Then,

        AC ≅ AD

Hence, ΔACD is a isosceles triangle.

And we know that the base angle of isosceles triangle are same.

So,

    ∠ACD ≅ ∠ADC  proved

idc

step-by-step explanation:

idk

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.