QuestionIf $\triangle ABC \sim \triangle XYZ$ , complete this proportion: $\frac{BC}{AC}=\frac{?}{?}$ . Choices are A, B, C, D, or E.

Studdy Solution

STEP 1

Assumptions1. Triangle ABC is similar to triangle XYZ. . The sides of the triangles are proportional.

STEP 2

The concept of similar triangles states that the ratios of the corresponding sides of similar triangles are equal. In other words, if $\triangle ABC \sim \triangle XYZ$ , then the ratios of their corresponding sides are equal.

STEP 3

Given the proportion $\frac{BC}{AC}$ , we need to find the corresponding sides in $\triangle XYZ$ .

STEP 4

The side BC in $\triangle ABC$ corresponds to the side YZ in $\triangle XYZ$ .

STEP 5

The side AC in $\triangle ABC$ corresponds to the side XZ in $\triangle XYZ$ .

STEP 6

Therefore, the proportion $\frac{BC}{AC}$ corresponds to $\frac{YZ}{XZ}$ in $\triangle XYZ$ .
The answer is D. $\frac{YZ}{XZ}$ .

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QuestionIf $\triangle ABC \sim \triangle XYZ$ , complete this proportion: $\frac{BC}{AC}=\frac{?}{?}$ . Choices are A, B, C, D, or E.

Studdy Solution

STEP 1

Assumptions1. Triangle ABC is similar to triangle XYZ. . The sides of the triangles are proportional.

STEP 2

The concept of similar triangles states that the ratios of the corresponding sides of similar triangles are equal. In other words, if $\triangle ABC \sim \triangle XYZ$ , then the ratios of their corresponding sides are equal.

STEP 3

Given the proportion $\frac{BC}{AC}$ , we need to find the corresponding sides in $\triangle XYZ$ .

STEP 4

The side BC in $\triangle ABC$ corresponds to the side YZ in $\triangle XYZ$ .

STEP 5

The side AC in $\triangle ABC$ corresponds to the side XZ in $\triangle XYZ$ .

STEP 6

Therefore, the proportion $\frac{BC}{AC}$ corresponds to $\frac{YZ}{XZ}$ in $\triangle XYZ$ .
The answer is D. $\frac{YZ}{XZ}$ .

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QuestionIf △ABC∼△XYZ\triangle ABC \sim \triangle XYZ△ABC∼△XYZ, complete this proportion: BCAC=??\frac{BC}{AC}=\frac{?}{?}ACBC​=??​. Choices are A, B, C, D, or E.

Studdy Solution

STEP 1

Assumptions1. Triangle ABC is similar to triangle XYZ. . The sides of the triangles are proportional.

STEP 2

The concept of similar triangles states that the ratios of the corresponding sides of similar triangles are equal. In other words, if △ABC∼△XYZ\triangle ABC \sim \triangle XYZ△ABC∼△XYZ, then the ratios of their corresponding sides are equal.

STEP 3

Given the proportion BCAC\frac{BC}{AC}ACBC​, we need to find the corresponding sides in △XYZ\triangle XYZ△XYZ.

STEP 4

The side BC in △ABC\triangle ABC△ABC corresponds to the side YZ in △XYZ\triangle XYZ△XYZ.

STEP 5

The side AC in △ABC\triangle ABC△ABC corresponds to the side XZ in △XYZ\triangle XYZ△XYZ.

STEP 6

Therefore, the proportion BCAC\frac{BC}{AC}ACBC​ corresponds to YZXZ\frac{YZ}{XZ}XZYZ​ in △XYZ\triangle XYZ△XYZ.The answer is D. YZXZ\frac{YZ}{XZ}XZYZ​.

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QuestionIf $\triangle ABC \sim \triangle XYZ$ , complete this proportion: $\frac{BC}{AC}=\frac{?}{?}$ . Choices are A, B, C, D, or E.

The concept of similar triangles states that the ratios of the corresponding sides of similar triangles are equal. In other words, if $\triangle ABC \sim \triangle XYZ$ , then the ratios of their corresponding sides are equal.

Given the proportion $\frac{BC}{AC}$ , we need to find the corresponding sides in $\triangle XYZ$ .

The side BC in $\triangle ABC$ corresponds to the side YZ in $\triangle XYZ$ .

The side AC in $\triangle ABC$ corresponds to the side XZ in $\triangle XYZ$ .

Therefore, the proportion $\frac{BC}{AC}$ corresponds to $\frac{YZ}{XZ}$ in $\triangle XYZ$ .
The answer is D. $\frac{YZ}{XZ}$ .