MAST Grade 8 Similarity and Congruence. Practice it free.

Students use transformations to show similarity and use informal arguments about angle relationships. This Grade 8 reporting domain maps to 3 practice skills and 8 representative questions from the playable bank.

Grade 8Testlet 113 mapped skills
What the test measures

Similarity and Congruence skills

  1. Use transformations to show similarity of two-dimensional figures.

  2. Use informal arguments to show relationships between angles.

  3. 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.

Practice by skill

Topics mapped to this domain

Isosceles triangle angles

Grade 810 questions

Polygon angle formulas

Grade 815 questions

Triangle angle sum

Grade 810 questions
Try it now

8 free questions · 0/0 correct

Practice playmedium

In △MNO\triangle MNO, ∠M\angle M and ∠O\angle O are congruent. The measure of ∠N\angle N is 105.2∘105.2^{\circ}. What is the measure of ∠M\angle M?

Each congruent angle is 180∘−105.2∘2=37.4∘\dfrac{180^{\circ} - 105.2^{\circ}}{2} = 37.4^{\circ}.

Practice playeasy

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

A heptagon has 77 sides: (7−2)×180=900°(7-2) \times 180 = 900°.

Practice playeasy

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

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

Practice playeasy

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

Let each congruent angle measure x∘x^{\circ}. Then 2x+118.6=1802x + 118.6 = 180, so x=180−118.62=30.7∘x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}.

Practice playeasy

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

A octagon has 88 sides: (8−2)×180=1080°(8-2) \times 180 = 1080°.

Practice playeasy

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

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

Practice playeasy

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

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

Practice playeasy

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

A nonagon has 99 sides: (9−2)×180=1260°(9-2) \times 180 = 1260°.

Keep practicing

Turn similarity and congruence into game time.

The MAST placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blaster Gate game coverBlaster GatePlay →Blitz Tanks game coverBlitz TanksPlay →Buzzer Beater game coverBuzzer BeaterPlay →
Related Common Core standards
8.G.A.5
Source and test overview
All MAST prepOfficial test source
Reporting categories

More Grade 8 domains

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