Math / Geometry

QuestionQuestion Shwibaypes
Determine if triangle $S T U$ and triangle $V W X$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT neceacerily drawn to scale.) Answer Anteript 1 iat di 2

Studdy Solution

STEP 1

What is this asking? Do triangles $STU$ and $VWX$ have the same shape, even if they're different sizes? Watch out! Don't assume similarity just because some angles or sides look the same – we need to prove it!
Also, the order of the letters in the triangle names matters!

STEP 2

1. Find if we have enough information
2. Check for Side-Angle-Side (SAS) similarity

STEP 3

We know two sides of triangle $STU$ ( $ST = 20$ and $SU = 26$ ) and one angle ( $\angle S = 49^\circ$ ).
We also know two sides of triangle $VWX$ ( $VW = 40$ and $WX = 40$ ) and two angles ( $\angle V = 49^\circ$ and $\angle W = 52^\circ$ ).

STEP 4

To prove similarity, we can use several methods like Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS).
Let's see if we can use SAS.

STEP 5

We have $\angle S = 49^\circ$ in triangle $STU$ and $\angle V = 49^\circ$ in triangle $VWX$ .
These angles are equal!
This is our matching angle.
Now we need to check the ratios of the corresponding sides around this angle.

STEP 6

The sides around $\angle S$ in triangle $STU$ are $ST = 20$ and $SU = 26$ .
The sides around $\angle V$ in triangle $VWX$ are $VW = 40$ and $VX$ .
Uh oh, we don't know $VX$ !
But we do know $VW = 40$ and $WX = 40$ . $VW$ corresponds to $ST$ , and we need to find the side that corresponds to $SU$ .

STEP 7

We don't have enough information to find $VX$ .
SAS similarity requires two corresponding sides and the included angle.
We only have one corresponding side and the included angle.
We can't use SAS here!
Let's think about the angles.
We know two angles of triangle $VWX$ : $\angle V = 49^\circ$ and $\angle W = 52^\circ$ .
The angles in a triangle add up to $180^\circ$ , so $\angle X = 180^\circ - 49^\circ - 52^\circ = 180^\circ - 101^\circ = 79^\circ$ .
We don't know any other angles in triangle $STU$ , so we can't use AA similarity either.
We can't use SSS because we don't know all three sides of either triangle.

STEP 8

We don't have enough information to determine if the triangles are similar.
We can't use AA, SAS, or SSS similarity.

Was this helpful?

QuestionQuestion Shwibaypes
Determine if triangle $S T U$ and triangle $V W X$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT neceacerily drawn to scale.) Answer Anteript 1 iat di 2

Studdy Solution

STEP 1

What is this asking? Do triangles $STU$ and $VWX$ have the same shape, even if they're different sizes? Watch out! Don't assume similarity just because some angles or sides look the same – we need to prove it!
Also, the order of the letters in the triangle names matters!

STEP 2

1. Find if we have enough information
2. Check for Side-Angle-Side (SAS) similarity

STEP 3

We know two sides of triangle $STU$ ( $ST = 20$ and $SU = 26$ ) and one angle ( $\angle S = 49^\circ$ ).
We also know two sides of triangle $VWX$ ( $VW = 40$ and $WX = 40$ ) and two angles ( $\angle V = 49^\circ$ and $\angle W = 52^\circ$ ).

STEP 4

To prove similarity, we can use several methods like Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS).
Let's see if we can use SAS.

STEP 5

We have $\angle S = 49^\circ$ in triangle $STU$ and $\angle V = 49^\circ$ in triangle $VWX$ .
These angles are equal!
This is our matching angle.
Now we need to check the ratios of the corresponding sides around this angle.

STEP 6

The sides around $\angle S$ in triangle $STU$ are $ST = 20$ and $SU = 26$ .
The sides around $\angle V$ in triangle $VWX$ are $VW = 40$ and $VX$ .
Uh oh, we don't know $VX$ !
But we do know $VW = 40$ and $WX = 40$ . $VW$ corresponds to $ST$ , and we need to find the side that corresponds to $SU$ .

STEP 7

STEP 8

We don't have enough information to determine if the triangles are similar.
We can't use AA, SAS, or SSS similarity.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionQuestion ShwibaypesDetermine if triangle STUS T USTU and triangle VWXV W XVWX are or are not similar, and, if they are, state how you know. (Note that figures are NOT neceacerily drawn to scale.) Answer Anteript 1 iat di 2

Studdy Solution

STEP 1

What is this asking? Do triangles STUSTUSTU and VWXVWXVWX have the same shape, even if they're different sizes? Watch out! Don't assume similarity just because some angles or sides look the same – we need to *prove* it!Also, the order of the letters in the triangle names matters!

STEP 2

1. Find if we have enough information2. Check for Side-Angle-Side (SAS) similarity

STEP 3

STEP 4

To prove similarity, we can use several methods like Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS).Let's see if we can use SAS.

STEP 5

We have ∠S=49∘\angle S = 49^\circ∠S=49∘ in triangle STUSTUSTU and ∠V=49∘\angle V = 49^\circ∠V=49∘ in triangle VWXVWXVWX.These angles are equal!This is our **matching angle**.Now we need to check the **ratios of the corresponding sides** around this angle.

STEP 6

STEP 7

STEP 8

We don't have enough information to determine if the triangles are similar.We can't use AA, SAS, or SSS similarity.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionQuestion Shwibaypes
Determine if triangle $S T U$ and triangle $V W X$ are or are not similar, and, if they are, state how you know. (Note that figures are NOT neceacerily drawn to scale.) Answer Anteript 1 iat di 2

What is this asking? Do triangles $STU$ and $VWX$ have the same shape, even if they're different sizes? Watch out! Don't assume similarity just because some angles or sides look the same – we need to prove it!
Also, the order of the letters in the triangle names matters!

1. Find if we have enough information
2. Check for Side-Angle-Side (SAS) similarity

To prove similarity, we can use several methods like Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS).
Let's see if we can use SAS.

We have $\angle S = 49^\circ$ in triangle $STU$ and $\angle V = 49^\circ$ in triangle $VWX$ .
These angles are equal!
This is our matching angle.
Now we need to check the ratios of the corresponding sides around this angle.

We don't have enough information to determine if the triangles are similar.
We can't use AA, SAS, or SSS similarity.