Download Geometry A Unit 1 Day 6 Notes 1.5 Equal Parts of Segments and

Geometry A Unit 1 Day 6 Notes
1.5 Equal Parts of Segments and Angles
I. Congruent - _________________________________ symbol: ___________
Congruent segments are segments that have the same length.
Congruent angles are angles that have the same measure.
We say that the measures segments and angles are equal, but the segments and angles are
congruent.
but
AB  BC
AB  BC
A. As you are told that parts are congruent, you should mark the diagram so that
all the known information is visible in one location.
A
4 cm
B. Don't assume that a picture is drawn to scale
or that you know something unless you have
been told.
B
5 cm
Ex: In the figure, AB  BC and CD  DA.
D
C
CD = ___________, DC  _____________
C. Other words can indicate that there are equal parts in a figure.
1. Midpoint - ____________________________________________________
________________________ If D is the midpoint of RC, then _____________.
Ex: In the diagram, M is the midpoint of TU. If mTU = 24 ft, MU = ________.
T
M
U
2. Bisect - ________________________________________________________.
a. Bisects - point or segment that is dividing a segment or angle into two equal parts
b. Bisected - angle or segment that has been divided into two equal parts
Ex: If AU bisects RS , and RU = 12.5 in, find RS.
R
U
S
RS = ___________
II. Equal Parts of Angles - How we'll know and what we can conclude.
1. We can be told explicitly.
a.  SUV   SUM. Find  SUV. _______
V
S
2. The angles can be marked with one, two …curves.
3. They can use the word "bisector".
Ex: Draw a diagram and answer the question.
U
M
Segment TV bisects  NTB. If  NTV = 61 , find m NTB . ___________
III. Group Practice: Answer the following questions the best you can. The answers are
provided at the end of the section, in no particular order. If your group can not find
your answer among those provided, ask your teacher to check your work.
1. In the diagram,  AMN is bisected by MQ and RS bisects  ABC. If  ABC = 142
and  QMA = 51 , find each of the following.
N
V
 ABR = _________  NMQ = _______
Q
C
R
M
A
 NMA = __________
B
S
2. Write an equation and solve for x.
8x - 2
12x - 18
3. Write an equation and solve for y.  ABC   CBD,
 ABC = 6y - 10, and
C
 ABD = 10y + 2
A
B
4, 11, 51, 71, 102
D
IV. Group Investigation
A. We've been trying to connect what you know to new ideas. Again, we'll set the tone for
what comes next by tapping into your existing skills.
1. Answer the following any way you want. Be ready to explain the thought behind
any answers your group comes up with.
What number is exactly in the middle of 0 and 18? ___________
What number is exactly in the middle of 0 and 17? ___________
What number is exactly in the middle of 2
1
and 14? __________
2
What number is exactly in the middle of 1 and 30? __________
What calculation can be done with any two numbers x1 and x2 to find the number
that is exactly in between them?
A little twist…
7 is exactly in the middle of 10 and what number? ____________
1 is exactly in the middle of 18 and what number? ____________
-7.5 is exactly in the middle of 5 and what number? _____________
V. The midpoint formula:
1. Working Forward
a. Find the midpoint of the segment
with endpoints A(-2, 10) and
B(4, 4).
2. Working Backwards
b. The midpoint of AC is (4, 5)
If point A is located at (5, -1),
find the coordinates of C.
The algebra should support the picture in both examples.
HW: Unit 1 Day 6 HW