QuestionSally's triangle has angles $50^{\circ}$ and $60^{\circ}$ ; Tom's has $50^{\circ}$ and $70^{\circ}$ . Are they similar?

Studdy Solution

STEP 1

Assumptions1. Sally constructs a triangle with two of the angles measuring $50^{\circ}$ and $60^{\circ}$ . . Tom constructs a triangle with two of the angles measuring $50^{\circ}$ and $70^{\circ}$ .
3. The Triangle Sum Theorem states that the interior angles of a triangle add up to $180^{\circ}$ .

STEP 2

First, we need to find the third angle for each triangle. We can do this by subtracting the sum of the known angles from $180^{\circ}$ .
For Sally's triangle $Third\, angle =180^{\circ} - (First\, angle + Second\, angle)$ For Tom's triangle $Third\, angle =180^{\circ} - (First\, angle + Second\, angle)$

STEP 3

Now, plug in the given values for the first and second angles to calculate the third angle for each triangle.
For Sally's triangle $Third\, angle =180^{\circ} - (50^{\circ} +60^{\circ})$ For Tom's triangle $Third\, angle =180^{\circ} - (50^{\circ} +70^{\circ})$

STEP 4

Calculate the third angle for each triangle.
For Sally's triangle $Third\, angle =180^{\circ} -110^{\circ} =70^{\circ}$ For Tom's triangle $Third\, angle =180^{\circ} -120^{\circ} =60^{\circ}$

STEP 5

Now that we have the measures of all three angles for each triangle, we can compare them. Two triangles are similar if they have the same angle measures.
ally's triangle has angles of $50^{\circ}$ , $60^{\circ}$ , and $70^{\circ}$ . Tom's triangle has angles of $50^{\circ}$ , $70^{\circ}$ , and $60^{\circ}$ .
Therefore, the two triangles must be similar.
The correct answer is (c) The triangles must be similar.

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