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SAT Congruence and Similarity



If point $$B$$ is the midpoint of $$\overline{AC},$$ $$x=42,$$ and $$y=115,$$ which of the following statements is NOT true?

(A) $$\ \ AB = CB$$
(B) $$\ \ \overline{DA} \cong \overline{EC}$$
(C) $$\ \ EB > DA > AB$$
(D) $$\ \ \triangle ABD \cong \triangle CBE$$
(E) $$\ \ \angle ADB + \angle CEB = 46$$



In the figure above, $$\overline{AE} \parallel \overline{BF}$$ and $$\overline{DE} \parallel \overline{FC}.$$ If $$AD = 13$$ and $$BC = 8,$$ which of the following is true?

$$\begin{array}{l l l l l} &\text{I.}\ P_{\triangle ADE} : P_{\triangle BCF} &=& 13:8\\ \\ &\text{II.}\ \frac{ED}{FC} = \frac{8}{13}\\ \\ &\text{III.}\ m\angle E : m\angle F &=& 1:1\\ \end{array}$$

(A) $$\ \$$I only
(B) $$\ \$$I and II only
(C) $$\ \$$I and III only
(D) $$\ \$$II and III only
(E) $$\ \$$I, II, and III only

A circle with center $$M$$ has area $$36\pi$$ and a circle with center $$N$$ has area $$81 \pi.$$ What is the ratio of the circumference of $$\bigodot M$$ to the circumference of $$\bigodot N?$$

(A) $$\ \ \frac{6}{15}$$

(B) $$\ \ \frac{6}{9}$$

(C) $$\ \ \frac{36}{81}$$

(D) $$\ \ 6$$

(E) $$\ \ 9$$

A triangle with sides lengths of $$5, 12$$ and $$10$$ is enlarged. If the new triangle is similar to the original, and the scale factor is $$7,$$ what is the perimeter of the new triangle?

(A) $$\ \ 12$$
(B) $$\ \ 27$$
(C) $$\ \ 105$$
(D) $$\ \ 189$$
(E) $$\ \ 1323$$



In the figure above, $$AB = 56, DE = 42,$$ and $$DC = 21.$$ What is the value of $$AC?$$

(A) $$\ \ \frac{28}{21}$$

(B) $$\ \ 14$$

(C) $$\ \ 21$$

(D) $$\ \ 28$$

(E) $$\ \ 56$$

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