Acute / Obtuse Isosceles Triangles - ISEE Upper Level: Quantitative Reasoning

Card 1 of 12

Didn't Know

Knew It

1 of 1211 left

Question

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Tap to reveal answer

Answer

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

← Didn't Know|Knew It →

Question

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

Tap to reveal answer

Answer

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to $3 \times 12 = 36$ inches, and 4 feet is equal to $4 \times 12 = 48$ inches. We choose 36 inches, since that, but not 48 inches, is a choice.

← Didn't Know|Knew It →

Question

The triangles are similar. Solve for .

Tap to reveal answer

Answer

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

← Didn't Know|Knew It →

Question

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Tap to reveal answer

Answer

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

← Didn't Know|Knew It →

Question

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

Tap to reveal answer

Answer

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to $3 \times 12 = 36$ inches, and 4 feet is equal to $4 \times 12 = 48$ inches. We choose 36 inches, since that, but not 48 inches, is a choice.

← Didn't Know|Knew It →

Question

The triangles are similar. Solve for .

Tap to reveal answer

Answer

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

← Didn't Know|Knew It →

Question

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Tap to reveal answer

Answer

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

← Didn't Know|Knew It →

Question

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

Tap to reveal answer

Answer

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to $3 \times 12 = 36$ inches, and 4 feet is equal to $4 \times 12 = 48$ inches. We choose 36 inches, since that, but not 48 inches, is a choice.

← Didn't Know|Knew It →

Question

The triangles are similar. Solve for .

Tap to reveal answer

Answer

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

← Didn't Know|Knew It →

Question

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Tap to reveal answer

Answer

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

← Didn't Know|Knew It →

Question

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

Tap to reveal answer

Answer

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to $3 \times 12 = 36$ inches, and 4 feet is equal to $4 \times 12 = 48$ inches. We choose 36 inches, since that, but not 48 inches, is a choice.

← Didn't Know|Knew It →

Question

The triangles are similar. Solve for .

Tap to reveal answer

Answer

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

← Didn't Know|Knew It →

Knew It

Acute / Obtuse Isosceles Triangles - ISEE Upper Level: Quantitative Reasoning

One of the base angles of an isosceles triangle is . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are . Let the measure of the third angle. Since the sum of the angles of a triangle is , we can solve accordingly:

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion. 3 feet is equal to inches, and 4 feet is equal to inches. We choose 36 inches, since that, but not 48 inches, is a choice.

The triangles are similar. Solve for .

Because the triangles are similar, proportions can be used to solve for the length of the side: Cross-multiply:

One of the base angles of an isosceles triangle is . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are . Let the measure of the third angle. Since the sum of the angles of a triangle is , we can solve accordingly:

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion. 3 feet is equal to inches, and 4 feet is equal to inches. We choose 36 inches, since that, but not 48 inches, is a choice.

The triangles are similar. Solve for .

Because the triangles are similar, proportions can be used to solve for the length of the side: Cross-multiply:

One of the base angles of an isosceles triangle is . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are . Let the measure of the third angle. Since the sum of the angles of a triangle is , we can solve accordingly:

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion. 3 feet is equal to inches, and 4 feet is equal to inches. We choose 36 inches, since that, but not 48 inches, is a choice.

The triangles are similar. Solve for .

Because the triangles are similar, proportions can be used to solve for the length of the side: Cross-multiply:

One of the base angles of an isosceles triangle is . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are . Let the measure of the third angle. Since the sum of the angles of a triangle is , we can solve accordingly:

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion. 3 feet is equal to inches, and 4 feet is equal to inches. We choose 36 inches, since that, but not 48 inches, is a choice.

The triangles are similar. Solve for .

Because the triangles are similar, proportions can be used to solve for the length of the side: Cross-multiply:

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply:

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

Because the triangles are similar, proportions can be used to solve for the length of the side:

$\frac{9}{3}=\frac{6}{x}$

Cross-multiply: