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# SAT Triangles

In $$\triangle ABC$$, $$m\angle A =20^\circ$$ and $$m\angle B = 35^\circ.$$ Which of the following is true?

(A) $$\ \ AC = AB > BC$$
(B) $$\ \ AC > BC > AB$$
(C) $$\ \ AB > AC = BC$$
(D) $$\ \ AB > AC > BC$$
(E) $$\ \ BC > AC > AB$$



In the figure above, points $$A, C,$$ and $$D$$ are collinear and $$\triangle ABC$$ is isosceles, with $$AB=BC.$$ If $$x=67,$$ which of the following is true?

(A) $$\ \ y = 113$$
(B) $$\ \ AC > AB+BC$$
(C) $$\ \ y < z$$
(D) $$\ \ x + y = 159$$
(E) $$\ \ BD > BA$$

The perimeter of $$\triangle ABC$$ is $$\frac{1}{4}$$ of the perimeter of $$\triangle DEF.$$ If $$\triangle ABC$$ is equilateral, and the perimeter of $$\triangle DEF$$ equals $$156,$$ what is the length of $$\overline{AB}?$$

(A) $$\ \ 4$$
(B) $$\ \ 13$$
(C) $$\ \ 39$$
(D) $$\ \ 52$$
(E) $$\ \ 156$$



In the figure above, the $$AD:DB = 2:19.$$ What is the ratio of the area of $$\triangle ADC$$ to the area of $$\triangle ABC?$$

(A) $$\ \ 2:19$$
(B) $$\ \ 2:21$$
(C) $$\ \ 19:21$$
(D) $$\ \ 4:361$$
(E) $$\ \ 4:441$$



In the figure above, $$a=60$$ and $$b=16.$$ What is the value of $$x+y?$$

(A) $$\ \ 16$$
(B) $$\ \ 44$$
(C) $$\ \ 76$$
(D) $$\ \ 104$$
(E) $$\ \ 208$$

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