Given: ab ≅ cd and ad ≅ bc prove: abcd is a parallelogram. statements reasons 1. ab ≅ cd; ad ≅ bc 1. given 2. ac ≅ ac 2. reflexive property 3. △adc ≅ △cba 3. ? 4. ∠dac ≅ ∠bca; ∠acd ≅ ∠cab 4. cpctc 5. ∠dac and ∠bca are alt. int. ∠s; ∠acd and ∠cab are alt. int. ∠s 5. definition of alternate interior angles 6. ab ∥ cd; ad ∥ bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3? triangle angle sum theorem sas congruency theorem sss congruency theorem cpctc
Dylan has built a simple clinometer by attaching a weighted string to the center of a protractor. he then attached a straw to the protractor to use as a sight. by looking at an object through the straw, dylan can determine the angle of elevation to that object. 1. dylan is using his clinometer to him determine the height of a tree. he stands 6m from the base of the tree and takes the measurement shown on the clinometer. then, he measures the height of his eye to be 1.6m above the ground a. sketch a diagram to represent this scenario.