Download 10/21 Triangles and Angles notes File

Unit 1B2 Day 1
Do now

Fill in the blank: If there is a line l and a point
P not on l, then __________________________
through P, parallel to l.
(Hint: It’s in your packet.)
Classifying Triangles

 A triangle is a figure formed by _________ segments
joining three ___________________ points.
 Classifying by sides
 Equilateral
 Isosceles
 Scalene
 Classifying by angles
 Acute
 Equiangular
 Right
 Obtuse
Note

An equilateral triangle is also
acute.
A triangle is equilateral if and only
if it is equiangular.
Classifying Triangles

Ex. 1: Classify the following triangles both by
sides and by angles.
Ex. 1A

Ex. 1a: Classify the triangle by sides
and by angles.
More Vocab.

 Each of the three points joining the sides of a triangle
is a _____________ (plural: ______________).
 Two sides that share a vertex are ___________________.
 The third side is considered _______________ that
vertex.
More Vocab.

 In a right triangle, the sides that form the right angle
are the _________.
 The side opposite the right angle is the ______________.
 In an isosceles triangle with exactly two congruent
sides, the two congruent sides are called the ________.
 The remaining side is called the ___________.
Ex. 2: Identifying Parts

 Classify the triangle both by sides and angles.
 Name the sides (hypotenuse, legs, base).
Ex. 2A

Ex. 2a: The diagram shows a bridge.
Classify triangle MNO by sides and angles.
Name the sides of triangle MNO.
Using Angle Measures

If you extend the sides of triangles, other
angles are formed.
Exterior
angles
Interior
angles
Triangle Sum Theorem (4.1)

The sum of the measure of the interior angles
of a triangle is _______.
Do Now

Complete the sentence with always, sometimes, or
never.
a) An isosceles triangle is ______ a right triangle.
b) An obtuse triangle is ______ a right triangle.
c) A right triangle is ______ an equilateral triangle.
d) A right triangle is ______ an isosceles triangle.
e) An equilateral triangle is _______ an acute triangle.
Exterior Angle Theorem (4.2)

The measure of an exterior angle of a triangle
is equal to the sum of the measure of the two
nonadjacent interior angles.
Ex. 3: Finding an Angle
Measure

Find the value of x. Then find the measure of
the of the exterior angle shown.
Ex. 3A

Ex. 3a: Find the value of x. Then find
the measure of the given exterior angle.
Corollary to the Triangle
Sum Theorem

A corollary to a theorem is a statement that
follows easily from the theorem.
Corollary to the Triangle Sum Theorem: The
acute angles of a right triangle are
_____________.
Ex. 4: Finding Angle
Measures

In a certain right triangle, the measure
of one acute angle is two times the
measure of the other. Find the measure
of both angles.
Ex. 4A

The measure of one acute angle of a right
triangle is one-fourth the measure of the
other acute angle. Find the measure of both
angles.
Ex. 5

 Find the measures of the numbered angles.
Closure

Can a scalene triangle be equiangular?
Can an isosceles triangle be obtuse?
Can a right triangle be equilateral?