Download 4-8-segments-in-a-triangle-median-perpendicular-bisector

Name:
Geometry Period
Date:
_
4-8 Notes
Lesson 4-7: Segments in a triangle
Learning Goal: What are the names and properties of segments in a triangle?
STATION 1: Altitude ( flashback)
Altitude -A segment from any vertex perpendicular to the line containing the opposite side (height)).
Altitude in an acute triangle
Altitude in a right triangle
Altitude in an obtuse triangle
Sometimes outside the triangle!
Guided Example:
Work:
4𝑥 − 6 = 90
+6 + 6
_______________________
4𝑥 = 96
𝑥 = 24
Steps:
1. Since AD is an altitude, it is perpendicular to
the that side of the triangle.
2. Perpendicular sides form 90° angles.
3. Set up an equation and solve for x.
.
.
Try one! Find the missing side. Show all of your work!
1) Put your answer in simplest radical form, if
In triangle PQR, PT is the altitude to QR . What is the value of x?
applicable.
** you’ll need to remember angle pair relationships here!!
STOP! Check-in with your GROUP!
STATION 2: Angle bisector ( flashback!)
Angle Bisector A line or segment that divides an angle in half
Guided Example:
m< PQS=5x-1ͦ , m<RQS=4x+7. If SQ is an angle
bisector of <PQR, solve for x and the measure of
<PQS.
Steps:
Work:
1)
5𝑥 − 1 = 4𝑥 + 7
𝑥=8
1) Since SQ is an angle bisector, the two bisected
angles are equal, set up an equation to solve for
x.
2) Substitute back in to solve for m<PQS
2) 5(8)-1=39
Try one! In the triangle shown below, OQ is an angle bisector. Solve for x and the measure of angle QOR.
Q
STOP! Check-in with your group!
STATION 3: Perpendicular bisector(flashback)
A perpendicular bisector is a line or segment that passes through the midpoint of a side and is perpendicular
to it.
BC is the perpendicular bisector of AD.
Note:
Perpendicular
bisectors do not
need to extend
from a vertex.
Guided Example:
BC is the perpendicular bisector of AD. Solve for x and the measure of AB.
Work:
Steps:
1. The segment is a perpendicular bisector, so
B must be a midpoint. A midpoint cuts a
segment into two equal sides.
1. 7x +10 = 9x -2
x=6
2. Substitute back in to length of AB and
simplify.
2. 7(6) +10
=52.
Try one!
Given that ED is a perpendicular bisector,
find x and the measure of AC.
E
STOP! Check-in with your group!
STATION 4: Median
Median-A segment joining any vertex to the midpoint of the opposite side.
Construction of a median:
1.
2.
Construct a perpendicular bisector to locate a
midpoint.
Draw a segment from vertex to midpoint.
Looks like:
Guided Example:
K
4x – 5
R
3x + 2
L
M
In triangle KLM,
MR
is the median to
KL .
If LR = 3x + 2 and RK = 4x – 5, what is the numerical value of LK?
Work:
Steps:
1. 3x+2 = 4x-5
X= 7
2. 3(7) +2 =23
23X2 = 46
LK =46
YOU TRY! In triangle KLM, construct the median to side KL
what is the numerical value of LK?
STOP! Check-in with your group!
1. The segment is a median, so R must be a
midpoint. A midpoint cuts a segment into
two equal sides.
2. Substitute back in to length of LR and
multiply by two since both segments are
congruent.
and label it MR . If LR = 2x – 4 and RK = 6x – 52,
STATION 5: Check-in as a CLASS
1) In each example below, name the type of line segment that CD is.
a)
b)
C
c)
d)
C
C
C
28 28
2”
A
D
B
A
D
2”
B
A
D
B
D
A
B
2)
3) In triangle DEF, DE  EF , EG bi sec ts DEF, D  ( x  5) and DEF  (3 x  10). Find the
measure of DEG.
Always draw
triangle first!
Mixed Practice
1. Polygon ABC is a triangle. CD is an altitude. CE is an angle bisector. CF is a median.
a) Name two congruent angles, each of which has its vertex at C.
b) Name two line segments that are congruent.
c) Name two line segments that are perpendicular to each other.
d) Name two angles that are right angles.
2.
Look at triangle ABC below.
B
F
E
C
D
What type of segments are AE, BD, and CF ?
a) perpendicular bisectors
b) medians
c) altitudes
d) angle bisectors
A