Problem Solution

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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…