of 0

Period: 1

Date: 12/16/16

# Median Property

Medians are segments that connect a vertex to the midpoint of the opposite side.

Step 1:

Look at what the question is asking you and find those two points in the triangle.

Step 2:

Find the vertex and draw a line to the opposite side midpoint.

AQ = QC

5x-4 = 3x+12

5x = 3x+18

2x = 18

x = 9

# C

AB = 4(9) - 11

AB = 36 - 11

AB = 25

### How To Find the Altitude in any Triangle

Altitudes are segments that are formed by drawing a segment from one side of the triangle to the opposite vertex. It is the shortest distance from to the vertex to the opposite side.

# Altitude Property

Step 1:

Find the vertex that was given to you.

Step 2:

Draw a line all the wat across to the opposite side to make a 90 degree angle.

# T

SR is an altitude of triangle RST. Solve for if m<SQR = 5x - 3 and m<TRQ = 4x + 3

# S

m<SRQ + m<TRQ = 90

5x-3 + 4x+3 = 90

5x+4x-3+3 = 90

9x+0 = 90

9x + 90

x = 10

# Angle Biscetor Property

Angle Bisectors are segments/rays/lines that bisects and angle of the triangle.

Step 1:

Find the angle that is given.

Step 2:

Draw a line that starts at the angle and goes through the opposite side.

m<KJL = m<IJL

x+66 = 9x+2

66 = 8x +2

64 = 8x

8 = x

# Example of Finding Angle Bisector

JL is an angle bisector of triangle IJK. m<KJL = x+66, m<IJL = 9x+2, and KJ = 2x-5. Determine x and KJ.

KJ = 2(8)-5

KJ = 16-5

KJ = 11

# Perpendicular Bisector Property

### Perpendicular bisectors are segments/rays/lines that pass through the triangle and are perpendicular to one side of the triangle.

Step 1:

Find the midpoint from the segment that you were given.

Step 2:

Draw a line from that midpoint straight up until you pass another side.

Step 3:

Draw a square at the bottom corner because you just made a 90 degree angle.

90 = 9x+2

88 = 8x

11 = x

3(11)-7

33-7

26

PR = 26*2

PR = 52

# 32,51,20

Triangle Inequality Theorem: the sum of any two sides of a triangle must be greater than the third.

32 + 51 > 20  *

32 + 20 > 51  *

20 + 51 > 32  *

AB + BC > AC

AB + AC > BC

AC + BC > AB

1 + 2 > 3

1 + 3 > 2

2 + 3 > 1

9 + 4 > 3  *

9 + 3 > 4  *

3 + 4 > 9  x

# SSS and SAS Inequality Theorems

Converse of Hinge Theorem (SSS Inequality):

Suppose you have two pairs of congruents sides in two different triangles.

Hinge Theorem (SAS Inequality):

Start with two pairs of congruent sides in two different triangles.