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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