Math  /  Geometry

QuestionDrag the blocks to complete the proofs.
Statements 1) 2) 18\angle 1 \cong \angle 8 3) 4) 816\angle 8 \cong \angle 16 5)
Reasons 1) given 2) 3) given 4) 5) Transitive prop. \cong
Linked slide Corresponding Angles <1<16<1 \triangleq<16 a|lb clld
Alt Ext Angles

Studdy Solution

STEP 1

What is this asking? We need to prove that two angles are the same size, using facts about parallel lines and what we're given. Watch out! Don't mix up the different types of angles (corresponding, alternate exterior, etc.)! Make sure you're using the right lines being parallel for each reason.

STEP 2

1. Set up the proof
2. Use corresponding angles
3. Use alternate exterior angles
4. Finish the proof

STEP 3

Alright, let's **begin**!
We're given that lines aa and bb are parallel (aba \parallel b), and lines cc and dd are parallel (cdc \parallel d).
Our **mission** is to prove that 116\angle 1 \cong \angle 16.
Let's write that down as our first and third statements!

STEP 4

So, statement 1 is "aba \parallel b" and the reason is "given".
Statement 3 is "cdc \parallel d" and the reason is also "given".
Awesome!

STEP 5

Now, look closely at 1\angle 1 and 8\angle 8.
Notice anything special?
They're **corresponding angles**!
Since aba \parallel b, corresponding angles are congruent.
That means 18\angle 1 \cong \angle 8.

STEP 6

Let's add that to our proof!
Statement 2 is "18\angle 1 \cong \angle 8" and the reason is "Corresponding Angles".
Boom!

STEP 7

Next up, check out 8\angle 8 and 16\angle 16.
What do you see?
They're **alternate exterior angles**!
Because cdc \parallel d, these angles are also congruent.
So, 816\angle 8 \cong \angle 16.

STEP 8

Let's put that in our proof.
Statement 4 is "816\angle 8 \cong \angle 16" and the reason is "Alt Ext Angles".
We're almost there!

STEP 9

Okay, we know 18\angle 1 \cong \angle 8 and 816\angle 8 \cong \angle 16.
Think of it like a chain: if A equals B, and B equals C, then A *must* equal C!
This is the **transitive property**.

STEP 10

So, our final statement is "116\angle 1 \cong \angle 16" and the reason is "Transitive prop. \cong".
We did it!

STEP 11

Statements 1) aba \parallel b 2) 18\angle 1 \cong \angle 8 3) cdc \parallel d 4) 816\angle 8 \cong \angle 16 5) 116\angle 1 \cong \angle 16
Reasons 1) given 2) Corresponding Angles 3) given 4) Alt Ext Angles 5) Transitive prop. \cong

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