Question

CE and FI are parallel. Giving reasons prove that DGH is isosceles

Answer 1

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Answer:

  ∠GDH = ∠GHD = 50°

Step-by-step explanation:

Angles FGD and EDG are alternate interior angles, so are congruent. That means angle EDG is 100°. The angle sum theorem tells us ...

  ∠EDG = ∠EDH +∠HDG

  100° = 50° +∠HDG

  50° = ∠HDG

You can find the measure of ∠DHG a couple of different ways. It is an alternate interior angle congruent to ∠EDH, so is 50°. It is one of two remote interior angles that have  a sum equal to the exterior angle FGD, so is ...

  ∠DHG = ∠FGD -∠HDG = 100° -50° = 50°

So, angles DHG and HGD both have measures of 50°. When a triangle has two angles with the same measure, it is an isosceles triangle.