Math  /  Geometry

QuestionREASONING Which of the following congruence statements are true? Select all that apply. TUUV\overline{T U} \cong \overline{U V} STVXVW\triangle S T V \cong \triangle X V W TVSVWU\triangle T V S \cong \triangle V W U VSTVUW\triangle V S T \cong \triangle V U W

Studdy Solution

STEP 1

What is this asking? Which triangles and sides are the same, given a diagram? Watch out! The order of the letters in triangle congruency matters!
Make sure you match corresponding angles and sides.

STEP 2

1. Analyze the given diagram
2. Check Congruency of Sides
3. Check Congruency of Triangles

STEP 3

Alright, awesome students, let's dive into this geometry puzzle!
We're given a diagram (not shown here, but you have it!), and we need to figure out which of those triangle and side relationships are actually true.

STEP 4

First, let's look at the statement TUUV\overline{TU} \cong \overline{UV}.
From the diagram, we see that TU=10TU = 10 and UV=12UV = 12.
Since 101210 \ne 12, we know that TU\overline{TU} and UV\overline{UV} have different lengths, so they are *not* congruent.

STEP 5

Now, let's investigate the triangle congruency statements.
Remember, for triangles to be congruent, their corresponding angles and sides must be congruent.

STEP 6

Let's start with STVXVW\triangle STV \cong \triangle XVW.
From the diagram, we see that SV=13SV = 13 and XV=15XV = 15.
Since 131513 \ne 15, these triangles are *not* congruent.

STEP 7

Next, let's check TVSVWU\triangle TVS \cong \triangle VWU.
We have TV=12TV = 12, VS=13VS = 13, and TS=5TS = 5.
For the other triangle, we have VW=13VW = 13, VU=15VU = 15, and UW=5UW = 5.
Notice that TVVWTV \ne VW and VSVUVS \ne VU.
So, these triangles are *not* congruent.

STEP 8

Finally, let's examine VSTVUW\triangle VST \cong \triangle VUW.
We have VS=13VS = 13, ST=5ST = 5, and TV=12TV = 12.
For the other triangle, we have VU=15VU = 15, UW=5UW = 5, and VW=13VW = 13.
Since VS=VWVS = VW, ST=UWST = UW, and TVTV is *not* equal to VUVU, these triangles are also *not* congruent.

STEP 9

None of the given congruence statements are true!

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