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