Congruent Triangles
CONGRUENT TRIANGLES
Chapter 4 ¨C Unit 6
SPRING 2019
GEOMETRY
Name ____________________________________Hour ______
Geometry
Classifying Triangles
4.1
Triangles can be classified by their _______________ and/or their ________________.
Objectives:
1) classify triangles
by their angle
measures and side
lengths
2) use triangle
classification to
find angle
measures and side
lengths
Triangle ABC use the symbol ?ABC
C
hypotenuse
Adjacent Sides
leg
Side opposite ?A
B
A
leg
Each point is a _______________________.
Example 4-1-1: Classify each triangle by its angles: acute, equiangular, obtuse, or right.
Example 4-1-2: Classify the Triangle by angle measures
a. ? BDC
b. ? ABD
Example 4-1-3: Classify the Triangle by side lengths
a. ? EHF
b. ? EHG
? , classify ????, ????, and ???? by
Example 4-1-4: If point M is the midpoint of ??
their sides: equilateral, isosceles, or scalene.
Example 4-1-6: Find the measures of the sides of isosceles triangle ABC
?? =
?? = ?? =
Example 4-1-7: If the perimeter is 47, find x and the length of each side. ? =_____
?? =_____
D
E
F
?? =_____
?? =_____
Why do you round the answer
down instead of rounding the
answer up?
Example 4-1-8: Real World Application
A steel mill produces roof supports by welding pieces of steel beams into equilateral
triangles. Each side of the triangle is 18 feet long. How many triangles can be formed
from 420 feet of steel beam?
Think and Discuss
Geometry
1
Geometry
Objectives:
1) find the measures
of interior and
exterior angles of
triangle
2) apply theorems
about the interior
and exterior
angles of triangles
Angle Relationships in Triangles
4.2
WARM-UP
1. What is the complement of an angle with measure 17¡ã?
2. How many lines can be drawn through a point not on a line, parallel to a given
line? Why?
Explore: Go to the last page and rip off the triangle,
then rip two of the corners and place them similar
to the example.
What conclusion can you draw about the sum of
the angles? ______________
What conclusion can you make about the exterior
angle compared to two of the angles?
Triangle Sum Theorem ¨C
Auxiliary line ?A line added to a diagram to help analyze the diagram. (Below:
???was added to make a line parallel to the ????
?? by the Parallel Postulate.)
Whenever you draw an auxiliary line, you must be able to justify its existence.
Give this as the reason: Through any two points there is exactly one line.
Geometry
2
Example 4-2-1: Real World Application
After an accident, the positions of cars are measured by law enforcement to
investigate the collision. Use the diagram drawn from the information collected to
find the indicated angle measures.
a. m? XYZ
b. ?? ???
Example 4-2-2: Real World Application The diagram
shows the path of the softball in a drill developed by
four players. Find the measure of each numbered angle.
?? 1 =
?? 2 =
?? 3 =
?? 1 =
?? 4 =
?? 7 =
?? 2 =
??5 =
?? 8 =
?? 3 =
?? 6 =
?? 9 =
Example 4-2-3: One of the acute angles in a right triangle measures 2x¡ã. What is the
measure of the other acute angle?
Exterior Angle ? the _________ formed by one side and an
_________ of the other side
In the picture, it is angle ________
Remote Interior ? the interior angles that are not
____________ to that exterior angle
In the picture, the angles are ____________
Geometry
3
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