Math  /  Geometry

QuestionTUWVUW.\angle T U W \cong \angle V U W .
Which term describes UW\overline{U W} ? perpendicular bisector altitude angle bisector median

Studdy Solution

STEP 1

What is this asking? If we cut an angle in half perfectly, what do we call the line that does the cutting? Watch out! Don't mix up angle bisectors with other special lines in triangles, like medians or altitudes.
They each have their own special jobs!

STEP 2

1. Understand Angle Bisectors
2. Analyze the Given Information
3. Identify UW

STEP 3

An **angle bisector** is a ray that splits an angle into two **perfectly equal** smaller angles.
Think of it as a precise cut right down the middle of an angle!

STEP 4

We're told that TUWVUW\angle T U W \cong \angle V U W.
This means that angle TUW is **congruent** to angle VUW.
Remember, congruent angles have the **same measure**!

STEP 5

So, the ray UW is splitting the larger angle TUV into two equal, smaller angles.

STEP 6

Since UW splits angle TUV into two congruent angles, it fits the **definition of an angle bisector** perfectly!

STEP 7

UW\overline{UW} is an **angle bisector**.

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