# Intermediate Geometry : How to find if two acute / obtuse triangles are similar

## Example Questions

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### Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Are the two triangles similar? If so, which postulate proves their similarity? (Figure not drawn to scale)

Yes; side-angle-side postulate

Yes; side-side-side postulate

Yes; angle-angle postulate

No, they are not similar

Yes; side-side-side postulate

Explanation:

The triangles are similar by the SSS postulate. The proportions of corresponding sides are all equal.

### Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

Are the two triangles similar? If so, which postulate proves their similarity? (Figure not drawn to scale)

No, the triangles are not equal

Yes, side-side-side postulate

Yes, angle-angle postulate

Yes, side-angle-side postulate

Yes, angle-angle postulate

Explanation:

The triangles are similar by the angle-angle postulate. 2 corresponding angles are equal to each other, therefore, the triangles must be similar.

### Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Are the two triangles similar? If so, which postulate proves their similarity? (Figure not drawn to scale)

Yes; side-side-side postulate

Yes; side-angle-side postulate

Yes; angle-angle postulate

No, the triangles are not similar

No, the triangles are not similar

Explanation:

The triangles are not similar, and it can be proven through the side-angle-side postulate. The SAS postulate states that two sides flanking a corresponding angle must be similar. In this case, the angles are congruent. However, the sides are not similar.

### Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

If the two triangles shown above are similar, what is the measurements for angles  and

Not enough information is provided.

Explanation:

In order for two triangles to be similar, they must have equivalent interior angles.

Thus, angle  degrees and angle  degrees.

### Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

Using the similar triangles above, find a possible measurement for sides  and .

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The original ratio of side lengths is:

Thus a similar triangle will have this same ratio:

### Example Question #6 : How To Find If Two Acute / Obtuse Triangles Are Similar

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths  and . What are possible measurements for the corresponding sides in triangle two?

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of side lengths for triangle one is:

Thus the ratio of side lengths for the second triangle must following this as well:

, because both side lengths in triangle one have been multiplied by a factor of

### Example Question #7 : How To Find If Two Acute / Obtuse Triangles Are Similar

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths  and . What are possible measurements for the corresponding sides in triangle two?

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of triangle one is:

Therefore, looking at the possible solutions we see that one answer has the same ratio as triangle one.

### Example Question #8 : How To Find If Two Acute / Obtuse Triangles Are Similar

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths  and . What are possible measurements for the corresponding sides in triangle two?

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of the side lengths in triangle one is:

If we take this ratio and look at the possible solutions we will see:

### Example Question #9 : How To Find If Two Acute / Obtuse Triangles Are Similar

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths mm and mm. What are possible measurements for the corresponding sides in triangle two?

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of triangle one is:

If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:

### Example Question #10 : How To Find If Two Acute / Obtuse Triangles Are Similar

Using the triangle shown above, find possible measurements for the corresponding sides of a similar triangle?

and

and

and

and

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of the triangle is:

Applying this ratio we are able to find the lengths of a similar triangle.

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