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Pre-Calculus Homework Solutions 122

# Pre-Calculus Homework Solutions 122 - 15 WP is an angle...

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15. WP is an angle bisector, so m HWP 1 2 m HWA . x 12 ¬ 1 2 (4 x 16) x 12 ¬ 2 x 8 12 ¬ x 8 20 ¬ x WP is a median, so AP PH . 3 y 11 ¬ 7 y 5 11 ¬ 4 y 5 16 ¬ 4 y 4 ¬ y m PAW ¬ 3 x 2 ¬ 3(20) 2 ¬ 58 m PWA m HWP because WP is an angle bisector. So, m PWA ¬ x 12 ¬ 20 12 or 32 m WPA m PAW m PWA ¬ 180 m WPA 58 32 ¬ 180 m WPA ¬ 90 WPA is a right angle, so WP is also an altitude. 16. WP bisects AH , so AP PH . 6 r 4 ¬ 22 3 r 3 r 4 ¬ 22 3 r ¬ 18 r ¬ 6 WP is perpendicular to AH , so m HPW 90. m WHA m HWP m HPW ¬ 180 8 q 17 10 q 90 ¬ 180 9 q 117 ¬ 180 9 q ¬ 63 q ¬ 7 m HWP ¬ 10 q ¬ 10 7 ¬ 17 17. Always; each median is always completely contained in the interior of the triangle, so the intersection point must also be inside the triangle. 18. sometimes; true for a right triangle but false for an equilateral triangle 19. Never; an angle bisector lies between two sides of the triangle and is contained in the triangle up to the point where it intersects the opposite side. so, the intersection point of the three angle bisectors must also be inside the triangle. 20. sometimes; true for an obtuse triangle but false for an acute triangle 21. PS is a median of PQR
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