section 5-1 and 5-2: midsegments and bisectors in triangles

Section 5-1 and 5-2: Midsegments and Bisectors in Triangles

March 5, 2012

Warm-up

Warm-up: Get your folder on side table and Pick up hand-out on side table

Complete “Investing Midsegments” handout: #1-16 (yes, you can write on it)

Warm-up

Section 5-1 and 5-2:

Midsegments and Bisectors in Triangles

Objectives: Today you will learn to use properties of midsegments perpendicular bisectors, and angle bisectorsto solve problems.

Section 5-1: Midsegments of Triangles

A midsegment of a triangle is a segment connecting the midpoints of two sides.

Triangle Midsegment Theorem: If 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. (p. 244)

DE is the midsegment of ΔABC

Section 5-1

Example 1: R is midpoint of and S is midpoint ofXY XZ

If YZ = 10, then RS = ____If RS = 7, then YZ = ____

Section 5-1

Example 2: R is midpoint of and M is the midpoint of Find value of x.

TY TS

Section 5-1

Example 3: R is midpoint of and M is the midpoint of Find value of x

TY YS

Section 5-1

Example 4: Given congruent segments as marked, find value of x

Section 5-1

Example 5: In ΔXYZ, M, N, and P are midpoints. The perimeter of ΔMNP is 60. Find NP, YZ and perimeter of ΔXYZ.

NP = ______

YZ = ______

Perimeter of ΔXYZ = ______

Section 5-1

Example 6: Given segments as marked, find x and y.

Section 5-1

Example 7: Given segments as marked, find all missing angle measurements

Section 5-2: Perpendicular Bisectors

A perpendicular bisector is a line or segment that is perpendicular to a segment at its midpoint.

Section 5-2: Perpendicular Bisectors (p. 249)

Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then the point is equidistance from the endpoints of the segment.

Converse of the Perpendicular Bisector Theorem: If a point is equidistance from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

Section 5-2: Angle Bisectors

Distance from a point to a line is the length of the perpendicular segment from the point to the line.

Section 5-2: Angle Bisectors (p. 250)Angle Bisector Theorem: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

Section 5-2:

Example 1: Given segments and angles as marked

AB = _____

CD = _____

Why?

Section 5-2:

Example 2: Given angles as marked

x = ____

FB = ____

FD = ____

CD = ____

Perimeter of CDFB = _______

How do you know?

Section 5-2: Real Life Example

Baseball (and Softball!)Diamonds are createdusing Angle Bisectors

Section 5-2:

Example 3: Given segments and angles as marked

x = _____

m∠GYE = ______

m∠GYO = ______

m∠RTY = ______

m∠YEG = ______

Reteaching 5-2: Practice Workbook, p. 55

Wrap-up Today you learned to use properties of

midsegments, perpendicular bisectors, and angle bisectors to solve problems.

Tomorrow you’ll learn about concurrent lines, medians and altitudes of a triangle

Homework pp. 246-247, #1-10, 13, 20-26, 32 pp. 251-253, #1-16, 46