7­39. 10 sides
b: regular decagon
7­40. If the diagonals intersect at E, then BE = 12 mm, since the diagonals are perpendicular bisectors. Then ΔABE is a right triangle and
AE = √152 ­ 122 = 9 mm. Thus, AC = 18 mm.
7­41. Yes, she is correct. One way: Show that the lengths on both sides of the midpoint are equal and that (2, 4) lies on the line that connects (­3, 5) and
(7, 3) .
7­42. (a) and (c) are correct because if the triangles are congruent, then corresponding parts are congruent. Since alternate interior angles are congruent, then AB // DE .
7­43. AB = √40 ≈ 6.32, BC = √34 ≈ 5.83, therefore C is closer to B.
1
Warm up
Write down the method and meanings on page 346 and write the definition down of a regular polygon on page 351
2
3
7 ­ 43
A
C
B
4
Lesson 7.2.1 What can congruent triangles tell me?
Objective: students will be introduced to proofs and will learn more properties
of parallelograms and kites
NOTE: first semester we studied triangles, now we are going to switch to QUADRILATERALS
In­class
7­44 learning properties about parallelograms
Part d) make a flowchart for showing that the two triangles are congruent
VERY IMPORTANT THAT YOU UNDERSTAND THIS
LEAVE ROOM ABOVE YOUR FLOWCHART TO ADD THINGS
7­45 There are a few things we need to add, once most groups are done I will
go over this with the whole class
7­46 Let's look at a KITE
7­47 looking at the other diagonal of a kite and using it to make a congruency flowchart
7­48 write down the properties you learned about parallelograms and kites
today
A
B
7­44
D
C
5
7­45
AB // CD
AD // BC
Given
<ADB ≅ <CBD
If lines are //, then
alternate interior angles
are ≅
Given
<ABD ≅ <CDB
BD ≅ BD
Reflexive property
If lines are //, then
alternate interior angles
are ≅
ΔADB ≅ ΔCDB
ASA ≅
6
C
7 ­ 47
A
AC ≅ BC
C
B
A
D
B
CD ≅ CD
m<ADC = m<BCD
Given
reflexive property Given ΔADC ≅ ΔBCD
SAS≅
AD ≅ DB
We will learn this
reason tomorrow
7
Homework: In Class 7 ­ 44 to 7 ­ 47
Review and Preview 7 ­ 49 to 7 ­ 53
FILL IN TOOLKIT FOR PARALLELOGRAM AND KITE
8