Fall Semester Final Preparation (proofs)

Proofs are worth 13 points on the Final. This is over 20%! You can do this! You can figure out proofs or at least get a lot of those 13 points! Normally you only have to figure out one side or the other - the statement or the reason. We will go over some tips.

• Got it

• I will try

• I hate proofs

The first step of a proof is always

• The given statements

• The introductory statements

• The summary statements

• The concluding statements

The last statement in the proof is always

• What you need to prove, it doesn't have to be written exactly how it is in the description though. If it is close that is good enough.

• What you need to prove in general terms

• Depends on the proof

• What you need to prove, written exactly how it is in the description.

Answer explanation

The only difference might be notation. "Angle ABC" can be written as <ABC or

$\angle ABC$ . They all mean the same thing.

The reflextive and symmetric properties are often mixed up. The reflexive property of equality states that a number is always equal to itself. (so examples 5 = 5, a = a, c = c, segment AC = segment AC, segment AC = segment CA (since segments can be named with either end first, right?)) The symmetric property of equality states values are still equal no matter which side of the equal sign they're on. Which of the following are showing the symmetric property? (Pick all that are correct)

• segment AB = 5, so 5 = segment AB

• a = b, so b = a

• a = a

• AB = BA

If you have a common side in a diagram. For example, AC in this diagram. AC is part of BOTH the upper triangle and the lower triangle. AC = AC or AC = CA is likely part of the proof! What is this property?

• Both are Symmetric Property of equality

• Both are Reflexive Property of equality

• Only AC = AC is the Reflexive Property of equality

• Only AC = AC is the Symmetric Property of equality

Answer explanation

BOTH are saying the segment is equal to itself.

BOTH are the reflexive property.

It might also have congruence symbols with segment lines over the letters. In this case, it is the "reflective property of congruence".

Tags

CCSS.HSG.SRT.B.5

You need to know the triangle sum theorem proof. (The sum of the angles in a triangle as up to 180 degrees) What the video to get the "outline" of the proof. What is the outline?

• Create a parallel line to one side, two pair of alternate exterior angles are congruent, angles in a line add up to 180 degrees.

• Create a perpendicular line to one side, two pair of alternate interior angles are congruent, angles in a line add up to 180 degrees.

• Create a parallel line to one side, two pair of alternate interior angles are congruent, angles in a line add up to 180 degrees.

• Create a parallel line to one side, two pair of alternate interior angles are congruent, angles in a line add up to 360 degrees.

Look at the image: What three angles add up to 180 degrees because they are in a line?

• 4, 2, and 5

• 4 and 2

• 2 and 5

• 4 and 1

• 1 and 3

Tags

CCSS.8.G.A.5

Look at the image: What angle is alternate interior to angle 4?

• 2

• 3

• 4

• 5

• 1

Answer explanation

Remember alternate interior angles are across the transversal, (but not a linear pair!) and still inside the parallel lines.

Tags

CCSS.8.G.A.5

Look at the image: What is the other set of alternate interior angles?

• angles 2 and 3

• angles 5 and 3

• angles 1 and 3

• angles 4 and 5

• angles 2 and 1

Tags

CCSS.8.G.A.5

If angle 1 is congruent to angle 4 can't I substitute angle 1 wherever angle 4 is and the "math" would be the same?

So, <4 + <2 + <5 = 180 would become:

• <4 + <1 + <5 = 180

• <1 + <2 + <5 = 180

• <4 + <2 + <1 = 180

• <2 + <3 + <5 = 180

• <3 + <2 + <5 = 180

Tags

CCSS.8.G.A.5