Download What theorem are the two triangles below congruent by?

4-1 Pumpkin Problems
This pumpkin needs to be carved into a Jack-O-Lantern. Follow the directions below to carve it.
1. The pumpkin’s LEFT EYE must be scalene. Show me it is scalene by putting measures on
it’s sides.
2. The pumpkin’s RIGHT EYE must be isosceles. Show me it is isosceles.
3. The pumpkin’s NOSE must be equilateral. Show me it is equilateral.
4. Finally, the pumpkin needs a mouth. Solve the following problem. The FINAL answer will
be how many teeth the pumpkin should have.
Find the measure of each side of equilateral triangle RST with RS = 2x + 2, ST = 3x, and TR = 5x - 4.
5. Color in the eyes, nose, and mouth in BLACK. Make sure you check with me to see if you
are correct FIRST! Then, color the rest of your Jack-O-Lantern however you wish!
Classifying Triangles
Define the following types of triangles, then draw a picture of each.
Equilateral
Scalene
Right
Obtuse
Equiangular
Isosceles
Acute
Acute Isosceles
Equilateral Equiangular
Right Scalene
Acute Scalene
Right Isosceles
Classify each triangle by angles AND sides. You will have 2 answers for each!
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4-1 Practice
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Classify each triangle as acute, equiangular, right or obtuse.
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Discovering the Angle Sum Theorem
Cut out the colored triangle. CAREFULLY tear (do not cut) off angles A, B, and C. Line up the angles so that they are adjacent to each other on
the line below. After your placement has been checked, glue your angles in place. Then answer the questions at the bottom of the sheet.
1. When you placed the angles of the triangle on the line beside each other, what did you notice?
2. If those 3 angles form a LINE, what must the sum of the interior angles of a triangle be? (What do all 3 of the angles add up to?)
Angle Sum Theorem- <A + <B + <C =
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Discovering the Exterior Angle Theorem
Cut out the colored triangle. Tear off angle A and B. Glue the two angles next to each other at the vertex of <ACD. They should be a perfect fit.
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B
C
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Exterior Angle Theorem- <A + <B = <ACD
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4-2 Practice
m1 = ________
m1 = ________ , m2 = ________
m1 = ________ m2 = ________
m1 = ________
m1 = ________
m1 = ______ , m2 = ______ , m3 = ______
m1 = ________
m1 = ______ , m2 = ______
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4-3 Practice
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4-4 Practice
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4-5 Practice
State the test that allows us to prove the triangles congruent. If the triangles are not congruent, write not possible.
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Pumpkin Glyph
Follow the directions below, showing all of your work:
Pumpkin:
Solve for x if the
triangle below is
isosceles and AB is
congruent to BC.
If the answer is 4, your pumpkin should be tall and skinny.
If the answer is 5, your pumpkin should be short and fat.
Eyes:
Solve for
If the answer is 106, your pumpkin should have round eyes.
If the answer is 74, your pumpkin should have triangular eyes.
If the answer is 56, your pumpkin should have square eyes.
<3.
Nose:
Solve for <3.
If the answer is 83, your pumpkin should have a round nose.
If the answer is 62, your pumpkin should have a triangular nose.
If the answer is 97, your pumpkin should have a square nose.
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Mouth:
In the congruency
statement below, what is
side RP congruent to?
If the answer is QR, your pumpkin should have 2 teeth.
If the answer is ST, your pumpkin should have 3 teeth.
If the answer is SU, your pumpkin should have 4 teeth.
Stem and Leaves:
What theorem are the two
triangles below congruent
by?
If the answer is SSS, your pumpkin should have a green stem
and 1 leaf.
If the answer is SAS, your pumpkin should have a brown
stem and 2 leaves.
If the answer is SSA, your pumpkin should have a brown
stem and 3 leaves.
Extras:
What are the angles in a
triangle that are NOT next
to the exterior angle?
If the answer is “remote interior angles”, your pumpkin
should have a ghost behind it.
If the answer is “alternate exterior angles”, your pumpkin
should have a witch’s hat.
If the answer is “vertical angles”, your pumpkin should have
a bat on top of it.
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SOL Practice
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9. What does CPCTC stand for?
10. Name the congruent angles AND the congruent sides in the congruency statement below:
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4-6 Practice
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
x = ________
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4-7 Practice
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