Side A B is parallel to Side D E in the map below.
Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet.
Which proportion solves for the distance between D and E?
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction
StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction
StartFraction 9 Over 6 EndFraction = StartFraction 15 Over x EndFraction
StartFraction 6 Over 15 EndFraction = StartFraction 9 Over x EndFraction
The proportion that solves for the distance between D and E is:
StartFraction 6 Over 15 EndFraction = StartFraction 9 Over x EndFraction
Which statements about the relationship between the two triangles below are true? Check all that apply.
Triangle A C D. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle R S T. Angle R is 74.9 degrees and angle S is 45.1 degrees.
Angle C is congruent to angle T
Angle C is congruent to angle S
Angle D is congruent to angle T
Triangle D C A is congruent to triangle T S R
Triangle D C A is similar to triangle T S R
Triangle C A D is similar to triangle T R S
Triangle C A D is congruent to triangle T R S
The statements that are true about the relationship between the two triangles are:
- Triangle D C A is congruent to triangle T S R
- Triangle C A D is similar to triangle T R S
The graph shows a line and two similar triangles.
On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.
Which expression finds the equation of the line?
StartFraction y Over x EndFraction = three-halves
StartFraction y Over x EndFraction = two-thirds
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
StartFraction y Over 3 EndFraction = StartFraction x Over 2 EndFraction
The expression that finds the equation of the line is:
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
The proportion that solves for the distance between D and E is StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction.
The proportion that solves for the distance between D and E is given by:
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction
To understand why this is the correct proportion, we can look at the properties of similar triangles and proportions. In the given map, it is mentioned that side AB is parallel to side DE, making triangle ABC and triangle CDE similar triangles.
Similar triangles are triangles that have the same shape but possibly different sizes. Corresponding sides of similar triangles are proportional. This means that if we take the lengths of corresponding sides, the ratios are equal.
In the given proportion, we compare the lengths of sides 9 and 6 in triangle ABC with the lengths of sides x and 15 in triangle CDE.
By setting up the proportion, we are saying that the ratio of the corresponding sides AB and CD is equal to the ratio of the corresponding sides BC and DE:
StartFraction AB Over CD EndFraction = StartFraction BC Over DE EndFraction.
Using the given measurements, we have:
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction.
By cross-multiplying and solving for x, we can find the distance between D and E.
So, the correct proportion to solve for the distance between D and E is:
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction.