In isosceles triangle DEF with DE cong DF, each base angle measures 58°. Which side has the greatest length?

DE and DF are equal and longest

OSTP Grade 11 CCRA Geometry Practice

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(8, 0)$ and $(8, 6)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|6 - 0| = 6\textsf{.}$ The radius is half the diameter, so $r = \dfrac{6}{2} = 3\textsf{.}$

Practice playmedium

The equation $x^2 + (y + 2)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $5$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, -2)$ and radius $4$ . Shifting down $5$ moves the center to $(0, -7)$ , so Circle B is $x^2 + (y + 7)^2 = 16$ .

Practice playeasy

A circle in the coordinate plane has equation $(x - 1)^{2} + (y - 4)^{2} = 81\textsf{.}$ What is the value of $r^{2}\textsf{?}$

In standard form the right side equals $r^{2}\textsf{,}$ so $r^{2} = 81\textsf{.}$

Practice playeasy

Find the volume of a cylinder with radius $3$ and height $2$ . Use $\pi = 3$ .

$V = \pi r^{2} h = 3 \times 9 \times 2 = 54$ .

Practice playeasy

In $\triangle ABC$ , $m\angle A=(x+8)°$ , $m\angle B=(2x+17)°$ , and $m\angle C=(x+55)°$ . What is the value of $x$ ?

The three interior angles sum to $180°$ : $(x+8)+(2x+17)+(x+55)=180$ , so $4x+80=180$ and $x=25$ .

Practice playeasy

In isosceles $\triangle DEF$ with $DE \cong DF$ , each base angle measures $58^{\circ}$ . Which side has the greatest length?

The base angles at $E$ and $F$ each measure $58^{\circ}$ , so the vertex angle at $D$ is $180^{\circ} - 2(58^{\circ}) = 64^{\circ}$ . The greatest angle is at $D$ , so the opposite side $EF$ is the longest.

Practice playmedium

A child who is $4$ feet tall casts a shadow $6$ feet long. A monument casts a shadow at the same time. If the monument is $30$ feet tall, how long is its shadow, in feet?

Set up $\dfrac{4}{6} = \dfrac{30}{s}$ . Cross-multiply: $4s = 180$ , so $s = 45$ feet.

Practice playeasy

A community pool is a rectangular prism $24$ feet long, $18$ feet wide, and $6$ feet deep when filled to the planned level. How many cubic feet of water does the pool hold at that level?

$V = \ell w h = 24 \times 18 \times 6 = 2{,}592$ cubic feet.

OSTP Grade 11 CCRA Geometry. Practice it free.

Geometry skills

proof and theorem use

transformations

triangle congruence and similarity

circles

geometric measurement and modeling

Topics mapped to this domain

Circle diameter endpoints to radius (SAT)

Circle equation translations (ACT/SAT/PSAT 8/9/10)

Equation of a circle

Surface area and volume

Algebra and polygon angle measures (ACT)

Geometric reasoning

Similar triangle shadows (ACT/SAT/PSAT 8/9/10)

Volume word problems (ACT)

8 free questions · 0/0 correct

Turn geometry into game time.

More Grade 11 CCRA domains