Geometry - 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

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:

$23:35=(23\times 4):(35\times 4)=92:140$

Tri_sim_vt_series_cont_

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

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.

$7:16=(7\times 3):(16\times3)=21:48$

Tri_sim_vt_series_cont_

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

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.

$29:33=(29\times 5):(33\times 5)=145:165$

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, they are not similar

Explanation

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

$\frac{3}{9}=\frac{1}{3}$

$\frac{4}{12}=\frac{1}{3}$

$\frac{6}{18}=\frac{1}{3}$

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

Yes, angle-angle postulate

Yes, side-side-side postulate

Yes, side-angle-side postulate

No, the triangles are not equal

Explanation

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

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

No, the triangles are not similar

Yes; side-side-side postulate

Yes; angle-angle postulate

Yes; side-angle-side postulate

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.

$\frac{12}{3}=4$

$\frac{18}{4}=4.5$

Sim._tri._vt_series

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

$a=75^\circ$ , $b=30^\circ$

$a=130^\circ$ , $b=30^\circ$

$a=37.5^\circ$ , $b=15^\circ$

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.

Sim._tri._vt_series

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

$3:8\rightarrow 3\cdot 2:8\cdot2\rightarrow 6:16$

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

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:

$5:7\rightarrow 5\cdot 3: 7\cdot 3=15:21$ , because both side lengths in triangle one have been multiplied by a factor of .

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?