techmathi - 4.5 - altitudes, medians, and bisectors

Bell Ringer

1. List the three things you need to use the HL Theorem.

2. In your own words, describe the isosceles triangle theorem.

3. List the four congruence theorems that will prove two triangles congruent.

Median

Picture: Both sides are congruent

The line that connects the vertex to the midpoint.

Median

EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

Midpoint-

If you have a midpoint- then the segments on both sides are CONGRUENT! That is why you will see the “tick marks”For the measure of the entire line- add both sides!

M D P

N

C

In MC and ND are medians.MNP,

1. What is NC if NP = 18?

9

2. If DP = 7.5, find MP. 15

A B C

E

D

1.What is ED if DC = 14?

2.What Is AC is BC is 9?

14

3.If BC = 3, find AC.

6

You Try the Following:

A E B

CD

If CD = 2x + 5, BD = 4x – 1, and AE = 5x –2, find BE.

In CE and AD are medians.ABC,

BD = CD 4x – 1= 2x + 5

2x = 6 x = 3

AE = BEBE = 5x – 2BE = 5(3) – 2

BE = 13

The intersection of the medians is called the CENTROID.

How many medians does a triangle have?

Draw the Picture:

When three or more lines or segments meet at the same point.

Concurrent:

Quick AssessmentWhat is a median?What is a centroid?What does concurrent mean?What is the vertex?What is a midpoint?

04/13/23

EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

Altitude

Picture:

04/13/23

EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

Altitude

The altitude is the “true

height” of the triangle.

Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of

the triangle.

Perpendicular Bisector

Picture:

Both sides are congruent- make sure you see this or it is NOT a perpendicular bisector

Tell whether each red segment is an perpendicular bisector of the triangle.