Question

similar figures
similar figures
find missing side length
show transcript
according to the video, similar figures have
the same shape and _______ sides.
a polygonal
b congruent
c proportional
what side does ac correspond to in the
example?
a side ab
b side df
c side bf
what is the value of x in the example?
a 5
b 7
c 9

Explanation:

First Question:

Similar figures have the same shape and their corresponding sides are proportional. Polygonal refers to the type of figure, congruent means equal in all aspects (not just sides for similar figures), so the correct option is about proportional sides.

In similar triangles (the example here with $\triangle ABC \sim \triangle DEF$ - assuming the notation), corresponding sides are matched by the order of the vertices. So AC (from A to C) should correspond to DF (from D to F) as per the similarity correspondence.

Step1: Identify the similar triangles and their corresponding sides.

Assume the first triangle has sides 3, 4, 5 (wait, no, looking at the first triangle: let's say $\triangle ABC$ with sides, maybe the first triangle has a side of length 4 (AC? Wait, no, the first triangle: let's see, the first triangle (left) has a base of 4, and the second triangle (right) has a base of 12. Let's assume the sides are proportional. Let's say the first triangle has a side of length 3 (AB) and the corresponding side in the second triangle is x? Wait, no, maybe the first triangle has sides: let's see, the left triangle: let's say sides are 3, 4, 5? No, wait, the problem is to find x. Let's assume the triangles are similar, so the ratio of corresponding sides is equal. Let's say the first triangle (let's call it $\triangle ABC$) has side BC = 4, and the second triangle ($\triangle DEF$) has side EF = 12. Another side of $\triangle ABC$ is AB = 3, and we need to find the corresponding side in $\triangle DEF$ (let's say DE = x). The ratio of BC to EF is $\frac{4}{12}=\frac{1}{3}$. So the ratio of AB to DE should also be $\frac{1}{3}$. So $\frac{3}{x}=\frac{1}{3}$? Wait, no, maybe I got the correspondence wrong. Wait, maybe the first triangle has a side of length 3 (AB) and the second triangle has a side of length x, and the base of the first is 4, base of the second is 12. So the ratio of the bases is 4:12 = 1:3. So the other sides should also be in 1:3. If the first triangle has a side of 3, then the second triangle's corresponding side is 33 = 9? Wait, no, wait, maybe the first triangle has a side of length 3, and the second triangle's corresponding side is x, and the ratio of the bases (4 and 12) is 1/3, so 3 / x = 4 / 12? Wait, no, cross - multiply: 4x = 312 → 4x = 36 → x = 9? Wait, no, that would be if 4 corresponds to 12, and 3 corresponds to x. Wait, 4/12 = 3/x → x = (312)/4 = 9? Wait, but let's check again. Wait, maybe the first triangle has sides: let's say the left triangle has sides 3, 4, and the right triangle has a base of 12, and we need to find the other side. The ratio of the bases is 4:12 = 1:3. So the other side (which is 3 in the first triangle) should be multiplied by 3 to get x. So 33 = 9? Wait, but the options are 5,7,9. So x = 9.

Step1: Determine the ratio of corresponding sides.

The length of the base of the first triangle (let's say side \( BC = 4 \)) and the base of the second triangle (side \( EF = 12 \)). The ratio of \( BC \) to \( EF \) is \( \frac{BC}{EF}=\frac{4}{12}=\frac{1}{3} \).

Step2: Apply the ratio to the corresponding side.

Let the side of the first triangle corresponding to \( x \) be \( AB = 3 \). Since the triangles are similar, the ratio of \( AB \) to its corresponding side (let's say \( DE=x \)) is the same as the ratio of \( BC \) to \( EF \). So \( \frac{AB}{DE}=\frac{BC}{EF} \). Substituting the values, we get \( \frac{3}{x}=\frac{4}{12} \).

Step3: Solve for \( x \).

Cross - multiply: \( 4x = 3\times12 \). So \( 4x = 36 \), and dividing both sides by 4 gives \( x=\frac{36}{4}=9 \).

Answer:

C. Proportional

Second Question: