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Problem Solutions

Part One: Geometry Worksheet 5.1A

Question 1

Median is line AB

Angle bisector is line CF

Altitude is line EDPerpendicular bisector is line BG

Question 2

Median is line HJ

Angle bisector is line LG

Altitude is line IK

Perpendicular bisector is line M

Question 3

Median is line BE

Angle bisector is line AD

Altitude is line CG

Perpendicular bisector is line DE

Question 4

Altitude is line CD

Medians are lines AF, BG, and CE

Question 5

Concurrent

Equidistant

Altitude

Question 5

Median

Question 7

If line AO is an Altitude, then angles AOC and AOB are right angles. If it is an angle bisector than angles CAO and BAO are equal. Two angles of triangle AOB are equal to two angles of triangle AOC. Therefore the third angles of these triangles must be equal. Angle ACB is therefore equal to angle ABC. Triangle ABC is thus an isosceles triangle with line AO as the axis of symmetry. The axis of symmetry in an isosceles triangle is usually the perpendicular bisector of the base. Line AO is therefore the median

Question 8

Isosceles triangle

Question 9

The height of a mid-wall when a ladder is placed on one side

Question 10

(3x+8) = (5x-6)14 = 2x and x= 7

Therefore, AC =(21+8)+(35-6)= 58

Question 11

Finding x

3x +6x +90 =180

9x=90

X=9

Finding y

10y-4=8y

2y=4

Y=2

Question 12

6x-9=4x=13

2x=22

X=11

Question 13

5x+8 =8x-16

24=3x

X=8

Question 14

6x+3= 7x-1

X=4

Question 15

Finding x

3x+3= 90

3x=87…

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