Download 5.3 Congruent Polygons and Cirlces

Warm-up
2/11/15
1) Given the set of blue lines are parallel and that
the red line is a transversal find the following
measures and then state how you know:
a) If m∠1 = 108° what is m∠3?
b) If m∠8 = 13° what is m∠7?
c) If m∠2 = 63° what is m∠6?
d) If m∠8 = 46° what is m∠2?
2) Give a congruence statement
for the following:
Announcements
2/11/15
1) Homework 5.1 and 5.2 must be handed into the
tray by the end of the period.
2) CM #26 today and retake CM #25.
3) I will be issuing detentions, so check missing
homework.
4) Unit quiz will be on Friday the 20th.
5) Extra 3% on test for anyone that brings in a
large Kleenex box. (Limit: 1 per person)
6) Homework Questions?
Warm-up
2/11/15
1) Given the set of blue lines are parallel and that
the red line is a transversal find the following
measures and then state how you know:
a) If m∠1 = 108° what is m∠3?
b) If m∠8 = 13° what is m∠7?
c) If m∠2 = 63° what is m∠6?
d) If m∠8 = 46° what is m∠2?
2) Give a congruence statement
for the following:
5.3 Congruent Polygons and
Circles
Congruent polygons are polygons that have three
properties:
1) Same number of sides.
2) Corresponding sides are congruent.
3) Corresponding angles are congruent.
Ex #1 Are these polygons congruent?
These two shapes have the same number of sides.
Their corresponding sides are congruent
since
Their corresponding angles are congruent
since
Writing congruent polygon statements:
To say these two triangles are congruent we need
to write it so the corresponding sides and angles
are in the correct order.
Since we can see that angle B corresponds to angle
E and angle C corresponds to angle F and angle A
corresponds to angle D then we need to write the
letters in this order:
△BCA ≅△EFD
Ex #2 Write a congruence statement for the
following shapes:
Ex #3
△ABC ≅△DCB
Warm-up
2/17/15
1) Given the set of blue lines are parallel and that
the red line is a transversal find the following
measures and then state how you know:
a) If m∠6 = 48° what is m∠2?
b) If m∠4 = 25° what is m∠2?
c) If m∠6 = 83° what is m∠5?
d) If m∠8 = 39° what is m∠2?
2) Give a congruence statement
for the following:
Announcements
2/17/15
1) Homework 5.3 Due Thursday
2) CM #24 on Wednesday.
3) CM #27 on Thursday
4) Unit quiz will be on Friday the 20th.
5) Extra 3% on test for anyone that brings in a
large Kleenex box. (Limit: 1 per person)
Cont of 5.3 Congruent Polygons
and Circles
Theorems
Theorem 5.10
The sum of the measures of the angles of any
triangle is 180°.
Theorem 5.11
If two angles of one triangle are congruent to two
angles of another triangle, then the third angles
are also congruent.
Theorem 5.12
The acute angles of a right triangle are
complementary.
Ex#4 Find the missing angle measure.
Ex #5 Find the x.
Ex#6 Find x.
Ex #7
If you have a quadrilateral, how many triangles
can you break this into?
So what would be the total angle measure of a
quadrilateral?
Total angle measure = 180° * 2
Total angle measure = 360
Ex#8
What would be the total angle measure of a
pentagon?
What would one angle of a regular pentagon be?
Angle measure of a regular n-gon = 180(n -2)/n
Ex #9 You are wanting to make a (late) valentines
card for the love of your life. You want it to be a
regular octagon like you saw in the store. What
angle should each angle of the octagon be so your
card is a perfect regular octagon?
Warm-up/Review for CM’s
2/18/15
1) Given the set of blue lines are parallel and that the red
line is a transversal find the following measures and then
state how you know:
a) If m∠1 = 108° what is m∠3?
b) If m∠8 = 13° what is m∠7?
c) If m∠2 = 63° what is m∠6?
d) If m∠8 = 46° what is m∠2?
2) a) Give a congruence statement
for the following:
b) Write 6 congruence
statements for the angles and
sides of each triangle.
3) a) What is the total angle measure for a heptagon?
b) What would be one angle measure of a regular
heptagon? (You must use the formula for each!)
Warm-up/Review for CM’s
2/19/15
1) a) Sketch a nonagon
b) Make line segments that go from vertex to
vertex but do not overlap. How many triangles is
the nonagon broken into?
c) What is the total angle measure for a nonagon?
d) What would be one angle measure of a regular
nonagon? (You must use the formula for each!)
Announcements
2/19/15
1) Homework 5.4 Due Tuesday.
2) Unit quiz will be on Friday the 20th.
3) Extra 3% on test for anyone that brings in a
large Kleenex box. (Limit: 1 per person)
Group-work
Here’s the deal:
1) Come grab slips of paper and 12 tacks.
2) In your group you will try to order the statements
and reasons given to you in the correct order.
3) You will then pin the papers to the wall.
4) This is not bases on speed, but rather correctness.
Extra credit on last Unit Quiz
-3 pts for correct proof.
-2 pts for 1 minor error.
-1 pt for 2 minor errors.
Your group will be DQ’ed if you look at another groups proof
or if you share info with another group or if a group member
is not contributing