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Geometry and Measurement

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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