2.4 proofs using similarity

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Today

You are able to use similarity to build simple proofs.

How are you doing today?

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Have you watched at least one of the instuctional video's I've linked in my study guide?

yes

no

01:55

You shouldn't think of axioms as being right or wrong—they define the rules of the game. You don't ask whether the rules of chess are right or wrong; if the game you are playing doesn't follow the rules of chess, that just means you aren't playing chess.

1 + 1 = 2 is a consequence of the rules of the game, it's not a rule itself.

03:48

Which of these is not a definition?

1. A straight angle measures 180 degrees.
2. A perpendicular bisector is a line that intersects a segment in its midpoint at a 90 degree angle.
3. In a parallellogram, the opposite sides are equal.
4. A parallellogram is a quadrilateral with two pairs of parallel sides.

04:58

Which of these statements is not a theorem/theory?

1. a​2​​+b​2​​=c​2​​
2. if a < b, then a < (a+b):2 < b
3. A hexagon is a six sided polygon.
4. The sum of all angles in a triangle is 180 degrees.

01:55

Which of these statements is not an axiom?

1. a+b=b+a
2. 1+1=2
3. a+(b+c)=(a+b)+c
4. a⋅b=b⋅a

Prove that

∠B​12​​=∠D​12​​

Prove that

Proof:

∠B​12​​=∠D​12​​

∠B​1​​=∠D​2​​(alternate)

Prove that

Proof:

∠B​12​​=∠D​12​​

∠B​1​​=∠D​2​​(alternate)

∠B​2​​=∠D​1​​(alternate)

Prove that

Proof:

∠B​12​​=∠D​12​​

∠B​1​​=∠D​2​​(alternate)

∠B​2​​=∠D​1​​(alternate)

∠B​1​​+∠B​2​​=∠D​1​​+∠D​2​​

Prove that

Proof:

∠B​12​​=∠D​12​​

∠B​1​​=∠D​2​​(alternate)

∠B​2​​=∠D​1​​(alternate)

∠B​1​​+∠B​2​​=∠D​1​​+∠D​2​​

∠B​1​​+∠B​2​​=∠B​12​​

∠D​1​​+∠D​2​​=∠D​12​​

Prove that

Proof:

∠B​12​​=∠D​12​​

∠B​1​​=∠D​2​​(alternate)

∠B​2​​=∠D​1​​(alternate)

∠B​1​​+∠B​2​​=∠D​1​​+∠D​2​​

∠B​1​​+∠B​2​​=∠B​12​​

∠D​1​​+∠D​2​​=∠D​12​​

∠B​12​​=∠D​12​​

qed

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