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

MCAP Geometry Similarity, Right Triangles, and Trigonometry Practice

Similarity, Right Triangles, and Trigonometry skills

G.SRT.A Understand similarity in terms of similarity transformations.

G.SRT.B Prove theorems involving similarity.

G.SRT.C Define trigonometric ratios and solve problems involving right triangles.

Standards basis

Maryland College and Career Ready Standards for Mathematics (MCCRSM) — Maryland

How the MCAP reports it

MCAP is Maryland's statewide successor to PARCC, built on the Maryland College and Career Ready Standards for Mathematics (which mirror CCSS-M) — it is not a Smarter Balanced administration despite the claims-style family resemblance. Each grade/course High Level Blueprint (September 2022) organizes the assessment into three subclaims: Content (23-24 one-point machine-scored items, listed per domain/conceptual category as MCCRSM cluster headings), Reasoning (6 items), and Modeling (6 items), the latter two defined by per-grade evidence statements and including constructed-response items. Cluster headings are transcribed verbatim from the blueprints, including their minor typographical deviations from the parallel CCSS-M headings; two evident misprints are normalized (a duplicated sentence fragment on 4.OA.C, and the domain codes printed as G.P.E / T.TF for G.GPE / F.TF). Since March 2025, grade 6-7 students enrolled in a high-school mathematics course may take the corresponding MCAP course assessment instead of the grade-level test.

Blueprint & weighting

Each High Level Blueprint (September 2022) publishes per-domain operational item counts. Content Subclaim (1-point machine-scored items): Grade 3 — OA 7, NBT 2, NF 7, Measurement 5, Geometry 2 (23 items); Grade 4 — OA 4, NBT 5, NF 10, Measurement 3, Geometry 1 (23); Grade 5 — OA 2, NBT 6, NF 9, Measurement 4, Geometry 2 (23); Grade 6 — RP 3, NS 8, EE 8, Geometry 2, SP 2 (23); Grade 7 — RP 8, NS 4, EE 5, Geometry 3, SP 3 (23); Grade 8 — NS 2, EE 10, Functions 5, Geometry 4, SP 2 (23); Algebra I — Number and Quantity 1, Algebra 12, Functions 9, Statistics 2 (24); Geometry — G.CO 7, G.SRT 8, G.C 3, G.GPE 3, G.GMD 1, G.MG 1 (23); Algebra II — Number and Quantity 3, Algebra 8, Functions 11, Statistics 1 (23). Every assessment adds 6 Reasoning Subclaim and 6 Modeling Subclaim operational items — four 1-point machine-scored each, plus two constructed-response items (two 3-point in grades 3-4; one 3-point and one 4-point in grades 5-8; two 4-point in Algebra I, Geometry, and Algebra II) — so a form carries 35 operational items (36 for Algebra I).

Official sources

MSDE — MCAP Mathematics (current program page: grades 3-8, Algebra I, Geometry, Algebra II)
MSDE — MCAP Overview / High Level Blueprints summary
MSDE — MCAP Grade 3 Mathematics High Level Blueprint (September 2022)

8 free questions · 0/0 correct

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

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 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 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 the standard coordinate plane, how many points are both $5$ units from the origin and also exactly $3$ units from the line $x = 0$ ?

Points $5$ units from the origin satisfy $x^{2} + y^{2} = 25$ . Being exactly $3$ units from $x = 0$ means $|x| = 3$ , so $x = 3$ or $x = -3$ . Substituting gives $y^{2} = 16$ , so $y = 4$ or $y = -4$ for each $x$ -value. That yields $(3, 4)$ , $(3, -4)$ , $(-3, 4)$ , and $(-3, -4)$ : $4$ points.

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

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

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

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $7$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $7$ .

MCAP Geometry Similarity, Right Triangles, and Trigonometry. Practice it free.

Similarity, Right Triangles, and Trigonometry skills

G.SRT.A Understand similarity in terms of similarity transformations.

G.SRT.B Prove theorems involving similarity.

G.SRT.C Define trigonometric ratios and solve problems involving right triangles.

Topics mapped to this domain

Geometric reasoning

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

Right triangle trig from two ratios

Special right triangles

8 free questions · 0/0 correct

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

More Geometry domains