Question

1. is △tuv ~ △wxv? explain.
2. higher order thinking are the triangles similar? explain.

Explanation:

Problem 5

Step1: Use vertical angles property

$\angle TVU = \angle WVX = 9x^\circ$

Step2: Set up equation for $\triangle TUV$

Sum of angles in triangle: $15x + (7x+12) + 9x = 180$
Simplify: $31x + 12 = 180$

Step3: Solve for $x$

$31x = 180 - 12 = 168$
$x = \frac{168}{31} \approx 5.42$

Step4: Calculate angles for $\triangle TUV$

$\angle T = 15x \approx 81.3^\circ$, $\angle U = 7x+12 \approx 49.9^\circ$, $\angle TVU \approx 48.8^\circ$

Step5: Calculate angles for $\triangle WXV$

$\angle W = 10x+15 \approx 69.2^\circ$, $\angle X = 180 - (9x + 10x+15) = 180 - (19x+15) \approx 62.0^\circ$, $\angle WVX \approx 48.8^\circ$

Step6: Compare corresponding angles

No matching set of 3 equal angles between the two triangles.

Step1: Find angles of first triangle

Sum of angles: $15x + 45x + 30x = 90x = 180$
Solve for $x$: $x = \frac{180}{90} = 2$
Angles: $15(2)=30^\circ$, $45(2)=90^\circ$, $30(2)=60^\circ$

Step2: Find angles of second triangle

Sum of angles: $6y + 9y + 3y = 18y = 180$
Solve for $y$: $y = \frac{180}{18} = 10$
Angles: $6(10)=60^\circ$, $9(10)=90^\circ$, $3(10)=30^\circ$

Step3: Compare corresponding angles

Both triangles have angles $30^\circ$, $60^\circ$, $90^\circ$.

Answer:

No, $\triangle TUV$ is not similar to $\triangle WXV$, because their corresponding angles are not all congruent.

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Problem 6