Math  /  Geometry

QuestionWhich two triangles are congruent by the SAS Theorem? Complete the congruence statement. Submit

Studdy Solution

STEP 1

What is this asking? Which two triangles are the same, like mirror images, because of two matching sides and the angle between them? Watch out! The angle has to be *between* the two sides, not just any angle!

STEP 2

1. Check the sides and angles of each triangle.
2. Find matching pairs.
3. Write the congruence statement.

STEP 3

Let's look at what we've got! VWX\triangle VWX has two sides marked with **one** and **two** tick marks, and the angle between them marked with an arc. JHI\triangle JHI *also* has two sides marked with **one** and **two** tick marks, and the angle between them marked with an arc. DEF\triangle DEF has sides marked with **two** and **three** tick marks, and an angle marked with an arc.

STEP 4

VWX\triangle VWX and JHI\triangle JHI both have matching sides and the angle *between* those sides is also matching!
That's exactly what we need for SAS (Side-Angle-Side). DEF\triangle DEF has a different combination of sides, so it's not a match for the others.

STEP 5

Since VWX\triangle VWX and JHI\triangle JHI are congruent, we can write it like this: VWXJHI\triangle VWX \cong \triangle JHI.
Notice how the order of the letters matters! VV matches with JJ (both opposite the side with two tick marks), WW matches with HH (both opposite the side with one tick mark), and XX matches with II (both at the marked angle).

STEP 6

VWXJHI\triangle VWX \cong \triangle JHI

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