SOL Geometry Reasoning, Lines, and Transformations Practice

Reasoning, Lines, and Transformations skills

undefined terms and postulates

proofs and logical reasoning

transformations in the coordinate plane

angle relationships and parallel lines

Standards basis

Virginia Mathematics Standards of Learning — Virginia

How the SOL reports it

Virginia SOL math is a state-specific assessment program built around the Virginia Mathematics Standards of Learning rather than a shared national test framework. It is aligned to Virginia grade-level and course standards, which are generally CCSS-like in organization but are published as Virginia-specific standards.

Blueprint & weighting

SOL uses the Independent / state-specific framework (by grade domains structure).

Official sources

Virginia Department of Education
VDOE — Standards of Learning for Mathematics (2023 SOL grade/course standards and assessment blueprints)
VDOE — SOL Test Blueprints (per-reporting-category item counts live inside the individual grade/EOC blueprint PDFs)

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?