GeoTrig Ch 2 Target 1

GeoTrig Ch 2 Target 1

Follow along with your notes in Notability as we learn the vocabulary for Unit 2

The goal:

T1: I can classify triangles by their angle measures and side lengths and apply this knowledge to write and solve equations to find angle measures and side lengths.

Triangles

• Definition: A triangle is a figure formed by connecting three noncollinear points with line segments.

• Naming Triangles: Triangles are named by the three points that form the triangle. The points are called the vertices of the triangle. All triangles have 3 sides and 3 angles To indicate you are naming a triangle you draw a triangle in front of the 3 capital letters.

Multiple Choice

Noncollinear means

• On the same line.

• NOT on the same line

• On the same plane

• Not on the same plane

Fill in the Blanks

Multiple Select

Which of the following are sides of this triangle?

• $\overline{OE}$

• $\overline{ONE}$

• $\overline{ON}$

• $\overline{NE}$

Naming parts of the triangle

• The vertices are O, N, E

•  The sides are $\overline{ON},\ \overline{NE},\ \overline{OE}$  

• The angles are  $\angle O,\ \angle N,\ \angle E$  

Classifying triangles by SIDES

• Scalene: NO sides are equal length.

• Isosceles: at least TWO sides are equal length.

• Equilateral: all THREE sides are equal length.

Multiple Choice

Looking at the tick marks, we know that this triangle is

• scalene

• isosceles

• equilateral

Multiple Choice

Looking at the tick marks, we know that this triangle is

• scalene

• isosceles

• equilateral

Multiple Choice

Looking at the tick marks, we know that this triangle is

• scalene

• isosceles

• equilateral

Classifying triangles by ANGLES

• Acute: All THREE angles are less than 90^o

• Right: ONE angle is 90^o

• Obtuse: ONE angle is greater than 90^o

Fill in all missing angles

Look for linear pairs.

Know that a triangle adds to 180^o.

Look for complementary angles.

Multiple Choice

Classify

 $\Delta ABD$  by its angles

• acute

• right

• obtuse

Multiple Choice

Classify

 $\Delta ADC$  by its angles

• acute

• right

• obtuse

Multiple Choice

Classify

 $\Delta BCD$  by its angles

• acute

• right

• obtuse

Multiple Choice

Classify this triangle by its sides

• scalene

• isosceles

• equilateral

Why use sides?

The tick marks are segment marks.

The expressions do not have degrees.

How do we solve for x?

There are two congruent sides so we set those expressions equal.

Fill in the Blanks

Finding the side lengths.

 $3x-0.4=x+1.4$ so
 $2x=1.8$  which means that $x=0.9$  

PQ = 0.9+0.1=1

RQ = 0.9+1.4=2.3 

RP = 3(0.9)-0.4 = 2.3

How do we solve for x?

There are three congruent sides so we set any two of those expressions equal.

Fill in the Blanks

Finding the side lengths.

 $\ \ \ 7n=10n-2.25\$             
 $-3n=-2.25$  

 $\ \ \ \ \ n=0.75$  

SU=7(0.75)=5.25
TU=10(0.75)-2.25=5.25
TS=2(0.75)+3.75=5.25

Example:

• Look at the tick marks: There are two congruent segments.

• Since segments EF and DF are congruent we know that

Multiple Select

Check the angles that must be congruent

•  $\angle D$  

•  $\angle E$  

•  $\angle F$  

Fill in the Blanks

Multiple Choice

What is the measure of

 $\angle E?$  

• 7

• 35

• 110

Equilateral triangles are equiangular

• Take 180 total degrees and divide by 3.

• Each angle is 60 degrees.

• Set 7x+4 = 60 and solve for x

Multiple Choice

x =

• 7

• 8

• 60

• 180