Let be the perpendicular to the line segment. Let and intersect in the point A. What is the measure of ∠PAY?

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Solution

From the figure, it can be easily observed that the measure of ∠PAY is 90°.

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Question 2

Let $¯ ¯¯¯¯¯¯ ¯ P Q$ be the perpendicular to the line segment $¯ ¯¯¯¯¯¯¯ ¯ X Y . L e t ¯ ¯¯¯¯¯¯ ¯ P Q a n d ¯ ¯¯¯¯¯¯¯ ¯ X Y$ intersect in the point A. What is the measure of $∠ P A Y$ ?

Q. Draw a line segment PQ= 8 cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meets PQ at point R. Measure the length of PR and QR. Is PR=QR?

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects line XY at point P at the same angle of inclination as AB. Line PQ is __ to line segment AB.

The steps to construct a triangle with given base angles $∠$ B and $∠$ C and BC + CA + AB, are:.
A. Draw a line segment, say XY equal to BC + CA + AB.
B. Make $∠$ LXY equal to $∠$ B and MYX equal to $∠$ C.
C. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A.
D. Draw perpendicular bisectors PQ of AX and RS of AY.
E. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

¯ ¯¯¯¯¯¯ ¯ P Q

is perpendicular to the line segment

¯ ¯¯¯¯¯¯¯ ¯ X Y

¯ ¯¯¯¯¯¯ ¯ P Q

and

¯ ¯¯¯¯¯¯¯ ¯ X Y

intersect at A. What is the measure of

∠

PAX and

∠

XAY.

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