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

This domain covers similarity, right triangle relationships, and trigonometric ratios. This Geometry reporting domain maps to 6 practice skills and 8 representative questions from the playable bank.

GeometrySimilarity, Right Triangles, and Trigonometry6 mapped skills
What the test measures

Similarity, Right Triangles, and Trigonometry skills

  1. understand similarity in terms of similarity transformations

  2. prove theorems involving similarity

  3. define trigonometric ratios and solve problems involving right triangles

  4. 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).

Practice by skill

Topics mapped to this domain

Geometric reasoning

Grade 910 questions

Law of sines and cosines

Grade 1215 questions

Right triangle trig from two ratios

Grade 1010 questions

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

Grade 810 questions

Special right triangle sides (ACT)

Grade 1215 questions

Special right triangles

Grade 1023 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

Parallel lines mm and nn are cut by a transversal. At one intersection, an angle measures 115∘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∘115^{\circ}.

Practice playeasy

In a 30°30°-60°60°-90°90° triangle, the short leg is 66. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×6=122 \times 6 = 12.

Practice playeasy

In a right triangle, cos⁡α=513\cos\alpha = \dfrac{5}{13} and tan⁡α=125\tan\alpha = \dfrac{12}{5}. What is sin⁡α\sin\alpha?

sin⁡α=tan⁡α⋅cos⁡α=125⋅513=1213\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 66 feet tall casts a shadow 44 feet long. A giraffe standing nearby casts a shadow at the same time. If the giraffe is 2121 feet tall, how long is its shadow, in feet?

Use 64=21s\dfrac{6}{4} = \dfrac{21}{s}. Cross-multiply: 6s=846s = 84, so s=14s = 14 feet.

Practice playeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is 22.22\textsf{.} What is the short leg?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is half the hypotenuse: 222=11.\dfrac{22}{2} = 11\textsf{.}

Practice playeasy

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, a leg is 9.9\textsf{.} What is the hypotenuse?

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, the hypotenuse is a leg times 2:\sqrt{2}\textsf{:} 92.9\sqrt{2}\textsf{.}

Practice playeasy

In △ABC\triangle ABC, the exterior angle at vertex CC measures 130∘130^{\circ}. If m∠A=48∘m\angle A = 48^{\circ}, what is m∠Bm\angle B?

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

Practice playeasy

In a 45°45°-45°45°-90°90° triangle, the hypotenuse is 525\sqrt{2}. What is each leg?

Each leg =hypotenuse2=522=5= \dfrac{\text{hypotenuse}}{\sqrt{2}} = \dfrac{5\sqrt{2}}{\sqrt{2}} = 5.

Keep practicing

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

The DC CAPE placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.SRT.D.10HSG.SRT.C.6HSG.SRT.C.8
The same skills on other tests
ATLASGeorgia MilestonesMCAPMO MAP
Source and test overview
All DC CAPE prepOfficial test source
Reporting categories

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