MO MAP Geometry Congruence Practice

Congruence skills

Experiment with transformations in the plane

Understand congruence in terms of rigid motions

Prove geometric theorems about lines, angles, triangles, and quadrilaterals

Standards basis

Missouri Learning Standards (Mathematics K-5 and Mathematics 6-12; revised standards approved April 19, 2016) — Missouri

How the MO MAP reports it

Missouri’s MAP math is built from the Missouri Learning Standards and the state’s item specifications, not from a separate national testing framework. The standards are closely CCSS-aligned in structure, with grade-level and course-level domains used as the native reporting/coverage structure.

Blueprint & weighting

Missouri publishes grade-level and EOC blueprints, but the accessible official pages in this pass did not expose the domain-by-domain percentage tables. The assessment page states that item specifications organize expectations by domains/strands and that blueprints are available for grade-level and EOC assessments.

Official sources

Missouri Department of Elementary and Secondary Education — Missouri Learning Standards
Missouri Department of Elementary and Secondary Education — Mathematics
Missouri Department of Elementary and Secondary Education — Assessment

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

Which transformation takes a line segment over a perpendicular bisector so that the segment maps directly onto itself?

A reflection is a rigid transformation that maps the points from a preimage, over a line of reflection, to the points of an image that are equidistant to the line. In this example, that line is the perpendicular bisector of a line segment from a point to its image, so the segment maps onto itself.

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 playeasy

Which transformation turns a figure $80^{\circ}$ around a fixed point so that all points remain equidistant from that point?

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage. In this example, that angle is $80^{\circ}\textsf{.}$

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 playeasy

Which transformation moves every point of a figure exactly $6$ cm in the same direction?

A translation is a rigid transformation that moves every point of a figure the exact same distance in the same direction. Since all points in the image remain equidistant from the points in the preimage, the figure remains congruent. In this example, that distance is $6$ cm.

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

Which transformation maps each point of a line segment over a perpendicular bisector so that they map onto the same line segment, keeping the image the same?