### All Intermediate Geometry Resources

## Example Questions

### Example Question #620 : Intermediate Geometry

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

**Possible Answers:**

Yes; side-angle-side postulate

Yes; side-side-side postulate

No, they are not similar

Yes; angle-angle postulate

**Correct answer:**

Yes; side-side-side postulate

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

### 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)

**Possible Answers:**

No, the triangles are not equal

Yes, side-side-side postulate

Yes, side-angle-side postulate

Yes, angle-angle postulate

**Correct answer:**

Yes, angle-angle postulate

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 #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)

**Possible Answers:**

Yes; side-angle-side postulate

No, the triangles are not similar

Yes; side-side-side postulate

Yes; angle-angle postulate

**Correct answer:**

No, the triangles are not similar

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 #3 : 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 ?

**Possible Answers:**

,

Not enough information is provided.

,

,

**Correct answer:**

,

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

Thus, angle degrees and angle degrees.

### Example Question #4 : How To Find If Two Acute / Obtuse Triangles Are Similar

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

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

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 #5 : 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?

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

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 #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?

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

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 #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?

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

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 #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 mm and mm. What are possible measurements for the corresponding sides in triangle two?

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

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 #9 : 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?

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

The ratio of the triangle is:

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

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