DC CAPE Geometry Similarity, Right Triangles, and Trigonometry Practice

Similarity, Right Triangles, and Trigonometry skills

understand similarity in terms of similarity transformations

prove theorems involving similarity

define trigonometric ratios and solve problems involving right triangles

apply trigonometry to general triangles

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

8 free questions · 0/0 correct

Practice playeasy

Parallel lines $m$ and $n$ are cut by a transversal. At one intersection, an angle measures $115^{\circ}$ . What is the measure of the corresponding angle at the other intersection?

When parallel lines are cut by a transversal, corresponding angles are congruent. The corresponding angle at the second intersection also measures $115^{\circ}$ .

Practice playeasy

In a $30°$ - $60°$ - $90°$ triangle, the short leg is $6$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 6 = 12$ .

Practice playeasy

In a right triangle, $\cos\alpha = \dfrac{5}{13}$ and $\tan\alpha = \dfrac{12}{5}$ . What is $\sin\alpha$ ?

$\sin\alpha = \tan\alpha \cdot \cos\alpha = \dfrac{12}{5} \cdot \dfrac{5}{13} = \dfrac{12}{13}$ .

Practice playmedium

At a zoo, a keeper who is $6$ feet tall casts a shadow $4$ feet long. A giraffe standing nearby casts a shadow at the same time. If the giraffe is $21$ feet tall, how long is its shadow, in feet?

Use $\dfrac{6}{4} = \dfrac{21}{s}$ . Cross-multiply: $6s = 84$ , so $s = 14$ feet.

Practice playeasy

In a $30$ - $60$ - $90$ triangle the short leg is $8$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 8 = 16$ .

Practice playeasy

In $\triangle ABC$ , the exterior angle at vertex $C$ measures $130^{\circ}$ . If $m\angle A = 48^{\circ}$ , what is $m\angle B$ ?

An exterior angle equals the sum of the two remote interior angles: $m\angle A + m\angle B = 130^{\circ}$ . So $m\angle B = 130^{\circ} - 48^{\circ} = 82^{\circ}$ .

Practice playeasy

In a $45°$ - $45°$ - $90°$ triangle, the hypotenuse is $5\sqrt{2}$ . What is each leg?

Each leg $= \dfrac{\text{hypotenuse}}{\sqrt{2}} = \dfrac{5\sqrt{2}}{\sqrt{2}} = 5$ .

Practice playeasy

In a right triangle, $\sin\theta = \dfrac{15}{17}$ and $\cos\theta = \dfrac{8}{17}$ . What is $\tan\theta$ ?

$\tan\theta = \dfrac{\sin\theta}{\cos\theta} = \dfrac{\dfrac{15}{17}}{\dfrac{8}{17}} = \dfrac{15}{17} \cdot \dfrac{17}{8} = \dfrac{15}{8}$ .

DC CAPE Geometry Similarity, Right Triangles, and Trigonometry. Practice it free.

Similarity, Right Triangles, and Trigonometry skills

understand similarity in terms of similarity transformations

prove theorems involving similarity

define trigonometric ratios and solve problems involving right triangles

apply trigonometry to general triangles

Topics mapped to this domain

Geometric reasoning

Law of sines and cosines

Right triangle trig from two ratios

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

Special right triangles

8 free questions · 0/0 correct

Turn similarity, right triangles, and trigonometry into game time.

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