5.1 Midsegments of Triangles

On April 18th, 1775 the signal was to tell Paul Revere whether the British were going to approach Lexington by sea or by land. A patriot placed two lamps in the tower and Paul Revere then spread the word to the rest of the patriots so they could be ready for the battle.

IF-LANDIF-IF-C

Can you figure out the puzzle below???

One if by land, two if by sea.

Theorem…

Theorem 5-1: Triangle Midsegment TheoremIf a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length

Midsegment of a Triangle: a segment connecting the midpoints of two sides of a triangle

Finding Lengths

In , H, J, and K are midpoints. Find HJ, JK, and FG.

EFG

AB = 10 and CD = 26. Find EB, BC, and AC.

Parallel Segments

In , A, B, and C are midpoints. Name the pairs of parallel segments.

*What theorem justifies that the lines are parallel?

DEF

Parallel Segments

Find and . Justify your answer.

VUZm

If XY = 3x + 2 and UV = 16, find the value of x.

XUVm

Real Life

is a new bridge being built over a lake as shown. Find the length of the bridge.

How long is the bridge in miles?

CD

Midterm Review

Find the next two terms in the following sequences.

5, 10, 20, 40

1,1

4,

1

9,

1

16

Find the midpoint and the distance between the following two points.

A(-2, 1) B(2, 4)

d(P1,P2) (x2 x1)2 (y2 y1)

2

M x1 x2

2,y1 y2

2

Midterm Review

2) What is another name for the plane Q?

*Why is plane EBD not an acceptable name for plane Q?*

Use the figure below to answer the following.

G

1) Find the intersection of AC and FG.

5.1 Midsegments of Triangles

HW (5.1) Pg. 262: #1, 4, 6, 7-11, 13, 14, 18, 20-22, 26, 34, 36

p.73: #36-37p.74: #1-3, 6-8

Space Invaders