Write proof in two-column form.
Given: , bisect each other. Prove: .
Vertically opposite angles
Property of Inequality If and then .
Two triangles and as shown below are the given triangles.
If two sides and one angle equal of two triangles are equal then from SAS corresponding triangles will be congruent triangles.
Since QR and ST bisect each other, therefore , .
The vertically opposite angles are always equal.
Therefore, . Then by SAS, .
Since then by CPCT .
Use exterior angle property as follows:
If and then .
Write the letters (a)-(d) in an order that completes an indirect proof of the statement: Through a point outside a line, there is at most one line perpendicular to the given line.
Given: Point P not on the line k.
Prove: There is at most one line through P perpendicular to k.
(a) But this contradicts corollary3 of theorem 3-11: In a triangle, there can be at most one right angle or obtuse angle.
(b) Then and are right angles, and has two right angles.
(c) Thus, our temporary assumption is false, and there is at most one line through P perpendicular to k.
(d) Assume temporarily that there are two lines through P perpendicular to k at A, B.
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