4.2: Angle Relationships in Triangles

Objectives:

• Find the measures of interior and exterior angles of triangles.

• Apply theorems about the interior and exterior angles of triangles.

Supplies: Math NotebookTextbook

Assignment: p. 228 #15-23(skip 17), 29-32

4.2: Angle Relationships in Triangles

•A line drawn connected to a shape to help write a proof.•In this case I have extended a side of a triangle to create an exterior angle.

An angle on the inside of a shape.

An angle that is created by extending a side of a shape.(in this picture, and the next, it is the angle mark in black)

•The two angles not connected to the created exterior angle. •Another way to say this is that they are the angles opposite the exterior angle.(In the picture the turquoise and purple angles.)

4.2: Angle Relationships in Triangles

Corollaries to Triangle Sum Theorem 4-2-2: The acute angles of a right triangle are

complementary. 4-2-3: If a triangle is equiangular, then each

angle measures 60°.

∠A+∠B+∠C=180°∠A+∠B=∠D

If ∠A=∠E and ∠B=∠F then ∠C=∠GH

K

∠H + ∠K=90°

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 mXYZ.

4.2: Angle Relationships in Triangles

mXYZ + mYZX + mZXY = 180°

Sum. Thm

mXYZ + 40 + 62 = 180 Substitute Property

mXYZ + 102 = 180 Simplify.

mXYZ = 78° Subtract 102 from both sides.

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 mYWZ.

4.2: Angle Relationships in Triangles

180-(62+40)=180-102=87180- (40+(12+87))=180-(40+99)=180-139=74

I just solved it! Can you rewrite my work in proof form and

provide justification for each step?

1 Bonus point on the next quiz if you can and do.

4.2: Angle Relationships in Triangles

The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

The measure of one of the acute angles in a right

triangle is 48 . What is the measure of the

other acute angle?

Statement Proof∠A+∠B=90° Acute angles of a right triangle are complementary∠A+∠63.7° =90° Substitution property∠A =26.3° Subtraction property of equality

90°-48 °=42If I asked you to write a proof and give you space on a quiz. Which one of these answers would get all 6 points? How many points would you give someone for the other answer?

4.2: Angle Relationships in Triangles

Find mB.

Given Justificationm∠A+m∠B= m∠BCD Exterior Angles Theorem15+2x+3= 5x-60 Substitution property2x+18= 5x-60 Simplification78=3x Subtraction property of equality26=x Division property of equalitym∠B= 2x+3 Givenm∠B= 2(26)+3 Substitutionm∠B= 55° Simplification.

4.2: Angle Relationships in Triangles

Find mACD.

Statement Justificationm∠ABC +m∠BAC =m∠ACD90°+(2z+1)°=(6z-9)°2z+91=6z-9100=4z25=zm∠ACD=(6z-9)m∠ACD=6(25)-9m∠ACD=141°

I provided the statements,

If You provide

justifications for each step,

Then you will receive

1 Bonus point on the next quiz.

4.2: Angle Relationships in Triangles

Find mK and mJ.

Statement Justificationm∠FKH= m∠IJG Third angles theorem4y =6y -40² ² Substitution property40=2y² Subtraction property of equality20= y² Division property of equalitym∠FKH=4y² Givenm∠FKH=4(20) Substitutionm∠FKH=80 Simplificationm∠IJG=80 Transitive property of equality

4.2: Angle Relationships in Triangles

Assignment:p. 228: 15-23(skip 17), 29-32