Congruent Triangles

CONGRUENT TRIANGLES

Chapter 4

GEOMETRY 2019-20 Name ____________________________________Hour ______

Objectives:

1) classify triangles by their angle measures and side lengths

2) use triangle classification to find angle measures and side lengths

Geometry

Classifying Triangles

4.1

Triangles can be classified by their _______________ and/or their ________________.

Triangle ABC use the symbol ABC

C Side opposite A

B

Adjacent Sides A

hypotenuse leg

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

c. HFG

Geometry

1

Example 4-1-4: If point M is the midpoint of , classify , , and by their sides: equilateral, isosceles, or scalene.

: ______________________ JKM: ______________________ KJL: _______________________

Example 4-1-5: 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 4-1-6: Coordinate Plane

Find the measures of the sides of KPL and classify each triangle by its sides. K(-3, -2) P(1, 3) L(3, -3) KPL is a ______________

KP =

PL =

KL =

Think and Discuss

Geometry

2

Objectives:

1) find the measures of interior and exterior angles of triangle

2) apply theorems about the interior and exterior angles of triangles

Geometry

Angle Relationships in Triangles

4.2

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

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 path of the softball in a drill developed by four players. measure of each numbered angle.

1 =

2 =

3 =

shows the Find the

3

 1 = 2 = 3 =

4 = 5 = 6 =

7 = 8 = 9 =

Example 4-2-3: One of the acute angles in a right triangle measures 2x?. What is the measure of the other acute angle?

Exterior Angle the __________ formed by one side and a _________ 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 ____________

Example 4-2-4: Find the in the fenced flower garden shown.

B Geometry

= ___________ Corollary A theorem that can be proven directly from another theorem.

A

Corollary 4.1 ? the acute angles in a right triangle are _________________ Corollary 4.2 ? there can be at most one right or obtuse angle in a triangle.

C

Corollary ? the angles in an Equiangular Triangle are ______________.

4

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