Transcript Warm UP - Greer Middle College Charter

WARM UP
Find the missing angles in the following triangles:
1.
Answer the following questions:
2.
3.
HOMEWORK ANSWERS
1. Yes
10. Yes
2. No
11. Yes
3. Yes
12. Yes
4. Yes
13. 4 < x < 14
5. Yes
14. 3 < x < 13
6. Yes
15. 4 < x < 16
7. Yes
16. 3 < x < 15
8. Yes
17. 3 < x < 19
9. Yes
18. 3 < x < 25
NOTES
Midsegment of a Triangle: a segment whose endpoints are the midpoints of two sides.
ACTIVITY 1: TRIANGLE MIDSEGMENTS
A
1. Draw Δ ABC.
2
C
1
4
3
B
2. Find the midpoints, M and N, of sides AB and AC. Then draw MN, the midsegment.
3. Measure and record MN and BC on your paper. What is the relationship between their
lengths?
4. Measure Ð1 and Ð2. Measure Ð3 and Ð4. What do your measurements suggest about
BC and MN? What postulate or theorem allows you to draw this conclusion?
5. Rewrite and complete the following conjecture:
Triangle Midsegment Conjecture
A midsegment of a triangle is _______________ to a side of the triangle and has a measure equal
to ___________________ of that side.
WHAT DOES IT MEAN FOR TWO FIGURES
TO BE CONGRUENT?
They must have the same:
• SIZE
• SHAPE
HERE’S THE SITUATION…
Prior to the start of a sailboat race, you (the judging official) must certify that all of the sails are the
same size. Without unrigging the triangular sails from their masts, how can the official (you)
determine if the sails on each of the boats are the same size?
•
With your group discuss and write down how you would go about doing this?
•
Over the next couple of classes we will be learning some geometry tricks (concepts) involving
triangles that will help us answer the above question.
•
Hand out materials
ACTIVITY 2: SSS POSTULATE
•
Using these three objects, create a triangle. (The three sides being the ruler, unsharpened
pencil and straightedge of the protractor.)
•
Compare your triangle with your group members triangles.
•
What do you notice?
•
Did everyone create the same triangle?
•
Are all of your triangles congruent?
• Yes
•
Why?
• All of the parts are the same or congruent.
•
Notice that we did not even pay any attention to the angles and they “took care of themselves”
•
Create another triangle using the three objects, but this time only using 8 inches of the ruler for
one of the sides.
•
Are all of your triangles congruent again?
• Yes
•
With your group discuss how we can use this concept to relate back to our initial problem with
the sailboats.
SSS (SIDE-SIDE-SIDE) POSTULATE
If the sides of one triangle are congruent to the sides of
another triangle, then the two triangles are congruent.
ACTIVITY 3: SAS POSTULATE
1. Draw a 6 cm segment.
2. Label it GH.
3. Using your protractor, make  G = 60.
4. From vertex G, draw GI measuring 7 cm long.
5. Label the end point I.
6. From the given information, how many different triangles can be formed?
7. Form  GHI.
8. Is your  GHI congruent to your group members  GHI.
9. What information was used to create this triangle?
10. Draw another segment this time 10 cm long.
11. Label it XY.
12. Using your protractor, make  X = 45.
13. From vertex X, draw XZ measuring 5 cm long.
14. Label the end point Z.
15. How many different triangles can be formed?
16. Form  XYZ.
17. Is your  XYZ congruent to your group members  XYZ?
18. What information was used to create this triangle?
SAS (SIDE-ANGLE-SIDE) POSTULATE
If two sides and the included angle in one triangle are
congruent to two sides and the included angle in another
triangle, then the two triangles are congruent.