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Question 1081439: Thank you for your help in advance.
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Prove the opposite angles of a parallelogram are congruent.
Prove the base angles of an isosceles triangle are congruent.
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Start with the following isosceles triangle. The two equal sides are shown with one red mark and the angles opposites to these sides are also shown in red.
The strategy is to draw the perpendicular bisector from vertex to segment .
Then use postulate to show that the two triangles formed are congruent.
If the two triangles are congruent, then corresponding angles to will be congruent.
Draw the perpendicular bisector from .
Since angle is bisected,we got
angle and angle which are same measure; so, angle
Segment ... ( This one was )
Segment (Common side is the same for both triangle and triangle )
Triangles and triangle are then congruent by or .
In other words, by
-angle()-
and
-angle()-
Since triangle and triangle are congruent, angle = angle
