geometry - math with mrs. solomon · 2020. 2. 26. · geometry 13.1 : side-splitting theorems p....
TRANSCRIPT
Geometry
13.1 : Side-Splitting Theorems
p. 774 - 780
mg Idea: When two transversals intersect parallel lines, proportional lengths are created.
If a line is parallel to a side of a triangle and intersectsthe other two sides in distinct points, it splits these sidesinto segments of proportional lengths.
e'Side-S - I ingtTheO em xarnJe.
Example 1Use lenghs as shown in the diagram at the right, in which jÉ ää
a. Find AE. b. Find DE
Solution
a. Since DE Il BC, pu can use fre Side-SplittingTheorem to calculate AE.AE
10
AE =b. The ratio of DE to BC is not the same as the rado of AD to DB or ofAEto
EC because Db and VC are not sides of Similar trianges must
be used. Since DÉ Il ÄC, by AA Similarihu As a
result, the raüos of corresponding lengths are equal.
DE
2.5 •
DE =
15m
10 an
B 18
t19PezL NSldes
Given m Il
Prove
rdpéi6V p I a-theorem
If a line parallel to the bases intersects the legs of atrapezoid and divides those legs into two segments.then the lengths of those segments are proportional.
I Ing
Proof Draw the diagonal ÄPofthe trapezoid, as shown atfre right
By the Triangle Side-SplittingTheorem applied to AACF,
By the Triangle Side-SplittingTheorem applied to AADF,
So, taking tie reciprocal of each side,
Thus, by the Transitive Property of Equality, b
COVERING THE IDEAS
Fill in the Blmk In 1-4, use the figure at the right to find a differentfraction equal to the given fraction.
5. In thetriangledtheright,igCHll
6. In the diagram below, the line segments are parallel to the
of the åiangle. for the lengths x, y, and z
2 2510
14 15
21
Side
13 NT28 mm H / J
30 mm
15 mm
SÖebaSC
7. A såident said, "I have an easy proof of the
Trapezoid Side-Splitting Iheorem, Use the figure
on the bottom of page 777. Start by translafing DF
so that the &anslaåon image of D is A. " finish
this suadent's proof. See margln.
8. In the diagram atthe right, t Il m Il n Il p.
Prove thatv=-z. See margin.
Back to Lesson 13-1
Name
Lesson Master
Objective A
In 1 and 2, find x and y.
Answer Page
Questions on SPUR ObjectivesSee Student Edition pages 819—821 for objectives.
In 3 and 4, determine what segments (if any) must be parallel.
1816 20
15
10
9.6
18 Y
tx)ø
Objective H
set is 7 feet above the ground. "Ille crossbar is 30 inches above the
ground. The legs are 8 feet long. How much of the leg is above
the crossbar, to the nearest inch?
6. In downtown Washington, D.C., Connecticut Avenue,JC-J
New Hampshire Avenue, K Street, and N Street
roughly form a large trapezoid. Assume M Street
runs parallel to K Street. Along New Hampshire Ave., z
the distance from K Street to M Street is 0.30 mile,
and from M Street to N Street is 0.26 mile. Along
Connecticut Ave., the distance from K Street to M L St NWStreet is 0.24 mile. Find the distance along
Connecticut Ave. from M Street to N Street. K St NW
, 30
12
10 L
N St NW
M St NW
Geometry 573
Back to Lesson 13-1 Answer Page
Name
Les son Master Questions on SPUR ObjectivesSee Student Edition pages 819-821 for objectives.
VOCABULARY
In 1 and 2, complete the Side-Splitting Theorem and its converse.
1. If a line is to a side of a triangle and intersects
the other two sides in distinct points, it splits these sides
into segments.
2. If a line intersects OP and OQ in distinct points X and Y so that
then XY is to PQ. -J L a H.8+X
Objective A1.4
3. In AJKLat the right, XYlljR. FindJX, rounded to the ne est tenth. €.(DH 4.72' x
4. In AXYZ at the right, Il ü. Find each missing length.
10
5. In the diagram at the right, h Il j Il k. Find each missing length.
30c. AB = 5y; DE = 12;
6. Given AADM at the right, in which OP Il AD, tell whether each
statement is true orfalse.
z
b. z
574 Geometry
4.8
x 8----
z
h
k
c
x z
O
Classwork
Find x,
3) In AABC, EFI ICE. Find x.
18
x+22
\ 7 X & 30
5) Determine whether BC I IDE.
BD- 9, BA: 27, and CEis one third of
No
2) Find x.
X + 12
4) Determine whether BC I IDE.
AD: 15, DB : 12, AE: 10, and EC- 8
yes Ito--lt6
COMMONLesson 4: Comparing the Ratio Method with the Parallel Method
s.25Date: 1/8/16CORE
0 2014 Common Core, Inc. Some rights reserved. commoncore.org
engageThis work is licensed under a
I Creative Commens Attribution-NgnCommercial-ShareAIike 3.0 Vnpgrted License.
Name: Date :
Geometry M2L4 Side Splitter Theorem HW Period:
1) Find x. 2) Find x.
24
30 10 30 10
30
3) If AD: 24, DB: 27, and EB- 18, find CE 4) Find x, QT, and TPif x + 6,
COMMONlesson 4:
CORE Date:
0 2014 Cornrnon Ccte. regs
SR: 12, 27 and 72: x -4.
1
IYO el SX
1/8/16 engageny s.26Comparing the Ratio Method with the Parallel Method
woo licensed underOjUY.uc.SA J
5) Determine whether Jl<l INM. 6) Determine whether Fäl IDÉ.
18, 30, KM: 21, and ML: 35 AE: 30, AC: 45, and AD is twice DB
Lesson Summary
Alifi€ splits two sides of triangle proportionally if and only if it is
parallel to the thitt$ Side
COMMON Lessm 4: Patellel Method
CORE engage s.27