11-20-2024 Triangle Midsegments & Perpendicular Bisectors

​Wonderful Wacky Wednesday
November 20, 2024

Draw

Look at the plexus, then determine at least THREE of the common sayings.

Get help from a neighbor if you need it : D

​Absences and Make-up Work

If a student is absent, to receive no grade deduction on classwork/homework, he or she must make up the work according to the following guidelines:

• If a student is absent the day an assignment is due and was not absent prior to the due date, he/she is expected to submit assignments the day of return.

• If a student is absent from school, he/she has 3 days from the day the student returns to school to make up the missed work.

• If a student is absent the day a test is given, he/she must make it up within one week, during courtyard or another designated time determined by the class facilitator, teacher, and the student.

 

Late Work for Students Present for the Assignment in Class

Late work will result in a 10 point deduction per day  (i.e. 1 day=10 point deduction; 2 days=20 point deduction; 3 days=30 point deduction).

● I can sketch and explain special segments in a triangle such

as:
○ Midsegments
○ Perpendicular bisectors
○ Medians
○ Altitudes

● I can identify and name pairs of similar triangles formed when

an altitude is drawn to the hypotenuse of a right triangle

● I can determine relationships among the angles and sides of a

triangle

Objectives

Essential Questions

● What segments have special purposes in

understanding triangles and solving problems?

● How do you solve problems that involve

measurements of triangles?

Why is This Important to Me?

Understanding special segments in triangles like midsegments,
perpendicular bisectors, medians, and altitudes, along with
recognizing relationships among angles and sides, is crucial for
deepening geometric comprehension and problem-solving abilities.

Vocabulary

Midsegments

●

Midsegment

Perpendicular Bisectors and
Angle Bisectors in Triangles

●

Angle bisector

●

Segment bisector

●

Perpendicular bisector of a line segment

●

Perpendicular bisector of a side of a triangle

Medians and Altitudes in

Triangles

●

Triangle Inequality Theorem

Inequalities in Triangles

●

Median

●

Centroid (point of concurrency)

●

Altitude

Midsegments

Midsegment of a Triangle

A segment that connects the midpoints of two sides
of a triangle.

The midsegment of a triangle is
1) parallel to the base
2) half the length.

DE is the midsegment of ΔABC,
If,

Then,
1) DE || AB
2) DE = ½ AB

Midsegments

Medians

A line segment connecting the midpoint of
one side of a triangle to the opposite vertex.

The medians of a triangle meet at a point.
Centroid (point of concurrency)

Midsegments

Draw

Put the word Midsegment in the middle star.

Write the definition of midsegment IN YOUR OWN WORDS.

You can use your notes from yesterday to complete the facts/characteristics.

Draw or search online for "real-world examples of triangle midsegments" to complete the examples and non-examples sections.

Guided Practice

Find:
1. FD

2. CB

3. The perimeter of ▵ABC

Midsegments

​Turn and Talk

What do you know about mid-segments?

• Share your thinking about ONE of the problems (1 minute)

• Then listen to your partner (1 minute)

• Continue taking until the time is up.

• At the end of the, I will spin the wheel for YOU AND YOUR PARTNER to BOTH share with the class.

Possible Sentence starters...
I can find the length of FD by ....
I can find the length of CB by ....
I can find the perimeter of ABC by ...
Since _____ is _____ I know that _____ is _____ because...

Guided Practice

Answer

Find:
1. FD

FD = EA = 10

2. CB

CB = 2(ED) = 2(8) = 16

3. The perimeter of ▵ABC

Add the three sides:
CB + BA + CA
= 16 + 6 + 6 + 10 + 10
= 16 + 12 + 20
= 48 units

Midsegments

Partner Practice:

Find the value of x and FD

Midsegments

Draw

With an elbow partner, solve x, then find the length of FD.

Independent Practice: Answers

Find the value of x and FD

Midsegments

Poll

What is your level of confidence with mid-segments?

Open Ended

Explain what a mid-segment of a triangle is and how it relates to the midpoints of the triangle's sides.

Open Ended

Find the length of CD.

• I can explain why the Perpendicular Bisector Theorem is true.

• I can use the perpendicular bisector theorem and its converse to find a missing angle or side in an isosceles triangle.​

​

​Learning Targets

​

Math Spoken Here!

Perpendicular Bisector: A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

https://study.com/academy/lesson/segment-bisector-theorem.html

Triangle Perpendicular Bisectors

Fill in the Blanks

Fill in the Blanks

G.7(A)
Exit Ticket Answers

Question: Answers Vary

Proportionality Relationships

Multiple Choice

What is the measure of Segment TP

• 3.5

• 7

• 14

• $$7\sqrt{2}$$