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Bell Work
a. What appears to be true about the lengths of the three tower
braces that form a triangle?
b. It also appears that the three angles of the triangles formed by
the braces are congruent. If this is true, what is the measure of
each of the angles?
c. If the braces formed noncongruent angles, could the lengths
of the braces still be congruent? Why?
Chapter 4 Congruent Triangles
4-1 Classifying Triangles
Essential Question:
How do I identify and classify triangles by angle measures
and side measures?
scalene triangle
isosceles triangle
equilateral triangle
equiangular triangle
acute triangle
right triangle
obtuse triangle
Summary
Homework
p. 239 #16-38 even
Exit
p. 244
Bell Work
a. What measurements other than the pivot angle must be programmed so
that the robot will move in a triangular path?
b. The pivot angles shown in the picture are all acute angles. Must each
pivot angle be an acute angle? Why?
c. Regardless of the robot's path, the sum of the measures of a the pivot
angles must always be the same. What is that sum?
4-2 Angles of Triangles
Essential Question:
How do I apply the Triangle Angle Sum Theorem
and the Exterior Angle Theorem?
exterior angles - formed by one side of the triangle
and the extension of an adjacent side.
Remote interior angles - not adjacent to the
exterior angle
corollary - a statement that can easily be proven
using a theorem
Summary
Homework
p. 248 #12-32 even
Exit
Bell Work
a. Why must the shape and size of the faceplate exactly match the space
where it fits?
b. What other parts of the faceplate must match the space where its fits
exactly?
c. What is the implication of the corresponding components of the faceplate
and the car stereo not matching exactly?
4-3 Congruent Triangles
Essential Questions:
How do I name and use corresponding parts of congruent
polygons?
How do I prove triangles congruent using the definition of
congruence?
Definition
Examples
Description
congruent
Non-Examples
Definition of Congruent Polygons
Two polygons are congruent if and only if their
corresponding parts are congruent.
Write the congruence statements.
Summary
Homework
p. 257 #10-22 even
Exit
Bell Work
Bell Work
Find x and y.
Discovery Activity
1. Supply
2. Builder
3. Writer
Exit
What have you discovered about congruent
triangles?
Bell Work
a. How is the board affected if the side arms are not the same
distance from the top of the board?
b. What must be true if ΔABC≅ΔXYZ?
c. How is the congruence of the triangles discussed affected if the
sides arms are not propositioned the same distance from the top of
the boards?
4-4 Proving Triangles Congruent - SSS and SAS
Essential Question:
How do I use the SSS and SAS Postulates to test for
triangle congruence?
Summary
Homework
p. 267 #6, 8, 10, 12, 16-18
Exit
Bell Work
Write the congruent statement.
4-5 Proving Triangles Congruent -ASA, AAS
Essential Question:
How do I use the ASA and AAS Postulates to test
for triangle congruence?
Summary
Homework
p. 276 #1, 4, 13, 14, 15
Exit
Write the congruent statement.
Bell Work
Bell Work
Are the triangles congruent? If they are
write the congruence statement and give
the reason.
Exit
What are you going to do to study for
the quiz tomorrow?
Bell Work
Are the triangles congruent? If they are
write the congruence statement and give
the reason.
Exit
How do you think you did on the quiz
and why?
Bell Work
a. Why are the triangles isosceles?
b. What appears to be true about the angles opposite the
equal sides?
c. What type of triangle results if the third side of the triangle
is congruent to the other 2 sides?
d. What do you think is true of the three angles if the three
sides are congruent?
4-6 Isosceles and Equilateral Triangles
Essential Question:
How do I use properties of isosceles and equilateral
triangles?
Find the value of x and y.
Find the value of x and y.
Summary
Homework
p. 287 #10-24 even
Exit
Find the value of each variable.