Math  /  Geometry

QuestionPoints: 0 of 1
Let ABCDEF\triangle A B C \cong \triangle D E F. Find mEm \angle E.
The value of mEm \angle E is \square { }^{\circ}. (Simplify your answer. Type an integer or a decimal.)

Studdy Solution

STEP 1

What is this asking? If triangle ABC is congruent to triangle DEF, what's the measure of angle E? Watch out! Congruent triangles mean matching angles and sides, but the triangles might be rotated or flipped!

STEP 2

1. Match Corresponding Angles
2. Find the Measure of Angle E

STEP 3

Alright, so we're told that ABCDEF\triangle ABC \cong \triangle DEF.
This little symbol \cong means **congruent**.
When triangles are congruent, it's like they're *identical twins*!
They have the same shape and the same size.
This means their corresponding angles are equal, and their corresponding sides are equal too!

STEP 4

The order of the letters matters *big time*!
Since ABC\triangle ABC is congruent to DEF\triangle DEF, angle AA corresponds to angle DD, angle BB corresponds to angle EE, and angle CC corresponds to angle FF.
It's like they're lined up for a dance!

STEP 5

The problem doesn't *directly* tell us the measure of angle EE.
Tricky, tricky!
But it *does* tell us the triangles are congruent.
And we know that corresponding angles of congruent triangles are equal.
So, if we can find the measure of angle BB, we've found the measure of angle EE too!

STEP 6

Looking back at the diagram, we see that mB=70m\angle B = 70^\circ.
Because angle BB corresponds to angle EE, we know that mEm\angle E *must* also be 7070^\circ!
We did it!

STEP 7

The measure of angle E is 70\bold{70^\circ}.

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