MCAP Geometry Congruence Practice — Sports Academy Games

Congruence skills

G.CO.A Experiment with transformations in the plane.

G.CO.B Understand congruence in terms of rigid motions.

G.CO.C Prove geometric theorems.

G.CO.D Make geometric constructions.

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 playmedium

In isosceles $\triangle DEF$ , the vertex angle measures $(4x+10)°$ and each base angle measures $(65-x)°$ . What is the measure of each base angle?

The three angles sum to $180°$ : $2(65-x)+(4x+10)=180$ , so $140+2x=180$ and $x=20$ . Each base angle is $65-20=45°$ .

Practice playmedium

In $\triangle GHI$ , $m\angle G=(2x+5)°$ , $m\angle H=(3x+5)°$ , and $m\angle I=(x+50)°$ . What is the measure of the largest angle of the triangle?

The angles sum to $180°$ : $(2x+5)+(3x+5)+(x+50)=180$ , so $6x+60=180$ and $x=20$ . The angles are $45°$ , $65°$ , and $70°$ , so the largest is $70°$ .

Practice playeasy

In parallelogram $PQRS$ , $m\angle P=(4x+6)°$ and $m\angle Q=(2x+24)°$ . What is the measure of $\angle P$ ?

Consecutive angles are supplementary: $(4x+6)+(2x+24)=180$ , so $6x+30=180$ and $x=25$ . Then $m\angle P=4(25)+6=106°$ .

Practice playeasy

Each interior angle of rectangle $WXYZ$ measures $(3x-12)°$ . What is the value of $x$ ?

Every interior angle of a rectangle measures $90°$ , so $3x-12=90$ and $x=34$ .

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

Two parallel lines are cut by a transversal. A pair of corresponding angles measure $(3x+16)°$ and $(2x+34)°$ . What is the measure of each of these angles?

Corresponding angles are congruent: $3x+16=2x+34$ , so $x=18$ . Each angle measures $3(18)+16=70°$ .

Practice playeasy

Two parallel lines are cut by a transversal. Same-side interior angles measure $(6x-5)°$ and $(4x+15)°$ . What is the value of $x$ ?

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$ , so $10x+10=180$ and $x=17$ .

Practice playeasy

Two parallel lines are cut by a transversal. A linear pair of adjacent angles measure $(5x+10)°$ and $(3x+50)°$ . What is the measure of the larger angle?