NJSLA Algebra I Congruence Practice

Congruence skills

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc

G-CO.A.2 Represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs

G-CO.B.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself

G-CO.B.4 Develop definitions of rotations, reflections, and translations

G-CO.B.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using rules and precise descriptions

G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure

G-CO.B.7 Use the definition of congruence in terms of rigid motions to decide if two figures are congruent

G-CO.C.8 Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions

G-CO.C.9 Prove theorems about lines and angles

G-CO.C.10 Prove theorems about triangles

G-CO.C.11 Prove theorems about parallelograms

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

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?

A linear pair is supplementary: $(5x+10)+(3x+50)=180$ , so $8x+60=180$ and $x=15$ . The angles are $85°$ and $95°$ , so the larger is $95°$ .

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 $3(18)+16=70°$ .

NJSLA Algebra I Congruence. Practice it free.

Congruence skills

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc

G-CO.A.2 Represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs

G-CO.B.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself

G-CO.B.4 Develop definitions of rotations, reflections, and translations

G-CO.B.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using rules and precise descriptions

G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure

G-CO.B.7 Use the definition of congruence in terms of rigid motions to decide if two figures are congruent

G-CO.C.8 Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions

G-CO.C.9 Prove theorems about lines and angles

G-CO.C.10 Prove theorems about triangles

G-CO.C.11 Prove theorems about parallelograms

Topics mapped to this domain

Algebra and polygon angle measures (ACT)

8 free questions · 0/0 correct

Turn congruence into game time.

More Algebra I domains