review: begin at the word “we”. every time you move, write down the word(s) upon which you land....
TRANSCRIPT
Review:
Begin at the word “We”. Every Time you move, write down the word(s) upon which
you land.
We
in
seven
days!
break
another
have
will
1. Move to the consecutive interior angle.2. Move to the alternate interior angle.3. Move to the corresponding angle.4. Move to the alternate exterior.5. Move to the exterior linear pair.
7. Move to the vertical angle.6. Move to the alternate exterior angle.
Triangles & Angle TheoremsTriangles & Angle Theorems
Learning Target:Students can prove geometric theorems involving lines, angles, triangles and parallelograms.
Learning Target:Students can prove geometric theorems involving lines, angles, triangles and parallelograms.
4.1 Classifying Triangles
Triangle – A figure formed when three noncollinear points are connected by segments.
E
DF
Angle
SideVertex
The sides are DE, EF, and DF.The vertices are D, E, and F.The angles are D, E, F.
Triangles Classified by AnglesAcute Obtuse Right
60º
50º
70º
All acute anglesOne obtuse angle
One right angle
120º
43º
17º
30°
60º
Triangles Classified by Sides
Scalene Isosceles Equilateral
no sidescongruent at least two
sides congruent
all sidescongruent
Classify each triangle by its angles and by its sides.
60°
60° 60°A B
C
45°
45°
E
F G
EFG is a right
isosceles triangle.
ABC is an acute
equilateral triangle
Adjacent Sides- share a vertex ex. The sides DE & EF are adjacent to E.
E
D F
Opposite Side- opposite the vertex ex. DF is opposite E.
Parts of Isosceles Triangles The angle formed by the congruent sides is called the vertex angle.
leg leg The congruent sides are called legs.
The side opposite the vertex is the base.
base anglebase angle
The two angles formed by the base and one of the congruent sides are called base angles.
Base Angles Theorem (4.9)
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If , thenACAB CB
Complete the Practice Problems
Converse of Base Angles Theorem (4.10)
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If , thenCB ACAB
Interior Angles Exterior Angles
Triangle Sum Theorem (4.1)Triangle Sum Theorem (4.1)The measures of the three interior angles
in a triangle add up to be 180º.
x°
y° z°
x + y + z = 180°
Complete the Practice Problems
The measure of the exterior angle is equal to the sum of two nonadjacent interior angles
1
2 3
m1+m2 =m3
Exterior Angle Theorem (4.3)Exterior Angle Theorem (4.3)
Complete the Practice Problems
Corollary to the Triangle Sum TheoremCorollary to the Triangle Sum Theorem
The acute angles of a right triangle arecomplementary.
x°
y°
x + y = 90º
Fill in the tableAcute Obtuse Right
Scalene
Isosceles
Equilateral