MAST Grade 8 Similarity and Congruence Practice

Similarity and Congruence skills

Use transformations to show similarity of two-dimensional figures.

Use informal arguments to show relationships between angles.

Standards: 8.G.4, 8.G.5

Standards basis

Montana PK-12 Mathematics Content Standards / Common Core State Standards for Mathematics (CCSS-M)-aligned Montana standards — Montana

How the MAST reports it

Montana’s MAST is a state-specific through-year assessment built by New Meridian and aligned to Montana’s academic content standards, not a Smarter Balanced-style claims/targets framework. The math blueprints organize content into grade-level strands/testlets that map directly to CCSS-M-derived Montana standards.

Blueprint & weighting

The blueprint publishes a through-year design of 12 strands/testlets per grade, with 1 strand per testlet, 2 reporting attributes per strand, and 9–13 items per testlet. It also specifies approximate item-type and DOK distributions, but does not publish percentage weighting by domain in the captured blueprint text.

Official sources

Montana OPI MontCAS
Montana OPI - MasteryGuide Mathematics Assessment Specifications and Blueprints
Montana OPI - Montana MAST Math Testlets

8 free questions · 0/0 correct

Practice playmedium

In $\triangle JKL$ , $\angle J$ and $\angle L$ are congruent. The measure of each of these angles is $61.7^{\circ}$ . What is the measure of $\angle K$ ?

The two congruent angles total $2 \times 61.7^{\circ} = 123.4^{\circ}$ , so $\angle K = 180^{\circ} - 123.4^{\circ} = 56.6^{\circ}$ .

Practice playeasy

What is $(6-2) \times 180$ ?

$(6-2) \times 180 = 4 \times 180 = 720$ .

Practice playeasy

If $m\angle A = 50^{\circ}$ and $m\angle B = 78^{\circ}$ in a triangle, what is $m\angle C\textsf{?}$

The sum of the interior angles of a triangle is $180^{\circ}\textsf{.}$ So $m\angle C = 180^{\circ} - 50^{\circ} - 78^{\circ} = 52^{\circ}\textsf{.}$

Practice playeasy

In $\triangle PQR$ , $\angle P$ and $\angle Q$ are congruent. The measure of $\angle R$ is $118.6^{\circ}$ . What is the measure of $\angle Q$ ?

Let each congruent angle measure $x^{\circ}$ . Then $2x + 118.6 = 180$ , so $x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}$ .

Practice playeasy

What is the sum of the interior angles of a hexagon?

A hexagon has $6$ sides: $(6-2) \times 180 = 720°$ .

Practice playeasy

The angles of a triangle measure $33^{\circ}\textsf{,}$ $88^{\circ}\textsf{,}$ and $k^{\circ}\textsf{.}$ What is the value of $k\textsf{?}$

The sum of the interior angles of a triangle is $180^{\circ}\textsf{.}$ So $k^{\circ} = 180^{\circ} - 33^{\circ} - 88^{\circ}\textsf{,}$ and $k = 59\textsf{.}$

Practice playeasy

In $\triangle XYZ$ , $\angle X$ and $\angle Z$ are congruent. The measure of $\angle Y$ is $52.6^{\circ}$ . What is the measure of $\angle X$ ?

The two congruent angles share the remainder equally: $\dfrac{180^{\circ} - 52.6^{\circ}}{2} = 63.7^{\circ}$ .

Practice playeasy

What is the sum of the interior angles of a heptagon?

A heptagon has $7$ sides: $(7-2) \times 180 = 900°$ .

MAST Grade 8 Similarity and Congruence. Practice it free.

Similarity and Congruence skills

Use transformations to show similarity of two-dimensional figures.

Use informal arguments to show relationships between angles.

Standards: 8.G.4, 8.G.5

Topics mapped to this domain

Isosceles triangle angles

Polygon angle formulas

Triangle angle sum

8 free questions · 0/0 correct

Turn similarity and congruence into game time.

More Grade 8 domains