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SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement Syllabus

The Quantitative Reasoning: Geometry and Measurement syllabus for SSAT (Secondary School Admission Test) in full: 4 chapters, 17 topics and 8 sub-topics, every one listed below, plus 50 Quantitative Reasoning: Geometry and Measurement flashcards with answers.

4Chapters
17Topics
8Sub-topics
50Flashcards

Quantitative Reasoning: Geometry and Measurement syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  1. Lines, Angles, and Polygons

     4 topics
    • Types of angles and angle relationships
      • Complementary and supplementary angles
      • Vertical angles
      • Angles formed by parallel lines and a transversal
    • Triangle classification and properties
      • Angle sum of a triangle
      • Equilateral, isosceles, and scalene
      • Exterior angle theorem
    • Quadrilaterals and their properties
    • Polygons and interior angle sums

  2. Perimeter, Area, and the Pythagorean Theorem

     5 topics
    • Perimeter of polygons
    • Area of triangles, parallelograms, and trapezoids
    • Circumference and area of circles
    • The Pythagorean theorem
      • Common Pythagorean triples
      • Finding a missing side of a right triangle
    • Composite and shaded-region figures

  3. Solid Geometry and Volume

     4 topics
    • Volume of prisms and cubes
    • Volume of cylinders
    • Surface area of rectangular solids
    • Nets and three-dimensional reasoning

  4. Measurement and Unit Conversion

     4 topics
    • Customary (U.S.) units of measure
    • Metric units and prefixes
    • Converting between units within a system
    • Elapsed time and calendar calculations

SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement flashcards — 50 questions with answers

  1. What is an acute angle, and what is the range of its measure?

    An acute angle measures more than $0^{\circ}$ but less than $90^{\circ}$ (i.e., $0^{\circ} < x < 90^{\circ}$).

  2. Define a right angle and a straight angle by their degree measures.

    A right angle measures exactly $90^{\circ}$; a straight angle measures exactly $180^{\circ}$.

  3. What is an obtuse angle, and what is the range of its measure?

    An obtuse angle measures more than $90^{\circ}$ but less than $180^{\circ}$ (i.e., $90^{\circ} < x < 180^{\circ}$).

  4. What are complementary angles and what do they sum to?

    Two angles are complementary if their measures add to $90^{\circ}$.

  5. What are supplementary angles and what do they sum to?

    Two angles are supplementary if their measures add to $180^{\circ}$.

  6. What is true about vertical angles formed by two intersecting lines?

    Vertical angles are the opposite angles formed by two intersecting lines, and they are always congruent (equal in measure).

  7. When a transversal crosses two parallel lines, what is the relationship between corresponding angles and between alternate interior angles?

    Both corresponding angles and alternate interior angles are congruent (equal).

  8. What do the three interior angles of any triangle sum to?

    They always sum to $180^{\circ}$.

  9. Classify triangles by their sides: scalene, isosceles, and equilateral.

    Scalene: all three sides different lengths. Isosceles: at least two sides equal. Equilateral: all three sides equal (and all angles $60^{\circ}$).

  10. Classify triangles by their angles: acute, right, and obtuse.

    Acute: all angles less than $90^{\circ}$. Right: one angle exactly $90^{\circ}$. Obtuse: one angle greater than $90^{\circ}$.

  11. In an isosceles triangle, what is true about the angles opposite the equal sides?

    The base angles (opposite the two equal sides) are congruent (equal in measure).

  12. State the Triangle Inequality Theorem.

    The sum of the lengths of any two sides of a triangle must be greater than the length of the third side: $a + b > c$.

  13. What is the relationship between an exterior angle of a triangle and the two remote interior angles?

    An exterior angle equals the sum of the two non-adjacent (remote) interior angles.

  14. What is the sum of the interior angles of any quadrilateral?

    $360^{\circ}$.

  15. What distinguishes a parallelogram, and what are two key properties of its sides and angles?

    A parallelogram has both pairs of opposite sides parallel. Opposite sides are equal, and opposite angles are equal (consecutive angles are supplementary).

  16. How is a rectangle defined and what is special about its diagonals?

    A rectangle is a parallelogram with four right angles. Its diagonals are equal in length and bisect each other.

  17. How does a rhombus differ from a general parallelogram?

    A rhombus is a parallelogram with all four sides equal; its diagonals are perpendicular bisectors of each other.

  18. What properties combine to define a square?

    A square has four equal sides and four right angles; it is both a rectangle and a rhombus, with equal, perpendicular diagonals that bisect each other.

  19. What defines a trapezoid (U.S. definition)?

    A trapezoid is a quadrilateral with exactly one pair of parallel sides (called the bases).

  20. What is the formula for the sum of the interior angles of a polygon with $n$ sides?

    $$S = (n-2)\times 180^{\circ}$$

Show the other 30 Quantitative Reasoning: Geometry and Measurement flashcards

  1. What is the measure of each interior angle of a regular polygon with $n$ sides?

    $$\frac{(n-2)\times 180^{\circ}}{n}$$

  2. What do the exterior angles of any convex polygon always sum to?

    $360^{\circ}$, regardless of the number of sides.

  3. What is the measure of each exterior angle of a regular polygon with $n$ sides?

    $$\frac{360^{\circ}}{n}$$

  4. How do you find the perimeter of any polygon?

    Add the lengths of all its sides.

  5. What are the perimeter formulas for a rectangle (length $l$, width $w$) and a square (side $s$)?

    Rectangle: $P = 2l + 2w$. Square: $P = 4s$.

  6. What is the formula for the area of a triangle?

    $$A = \frac{1}{2}bh$$ where $b$ is the base and $h$ is the perpendicular height.

  7. What is the area formula for a parallelogram?

    $$A = bh$$ where $b$ is the base and $h$ is the perpendicular height (not the slanted side).

  8. What is the area formula for a trapezoid with parallel bases $b_1$ and $b_2$ and height $h$?

    $$A = \frac{1}{2}(b_1 + b_2)\,h$$

  9. What are the formulas for the area of a rectangle and a square?

    Rectangle: $A = l\times w$. Square: $A = s^{2}$.

  10. What is the formula for the circumference of a circle, using radius $r$ and using diameter $d$?

    $C = 2\pi r$ or equivalently $C = \pi d$.

  11. What is the formula for the area of a circle?

    $$A = \pi r^{2}$$ where $r$ is the radius.

  12. What is the relationship between the diameter and radius of a circle?

    The diameter is twice the radius: $d = 2r$, so $r = \frac{d}{2}$.

  13. State the Pythagorean theorem and identify which side is the hypotenuse.

    $$a^{2} + b^{2} = c^{2}$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse (the side opposite the right angle, always the longest).

  14. Name two common Pythagorean triples used to identify right triangles.

    $3$-$4$-$5$ and $5$-$12$-$13$ (also $8$-$15$-$17$ and multiples like $6$-$8$-$10$).

  15. How do you find the length of a leg of a right triangle given the hypotenuse $c$ and other leg $b$?

    $$a = \sqrt{c^{2} - b^{2}}$$

  16. What is the general strategy for finding the area of a composite figure?

    Break it into familiar shapes (rectangles, triangles, circles), find each area separately, then add them together.

  17. How do you find the area of a shaded region inside a larger figure?

    Subtract the area of the unshaded (inner) shape from the area of the larger (outer) shape.

  18. What is the formula for the volume of a rectangular prism?

    $$V = l \times w \times h$$ (length times width times height).

  19. What is the formula for the volume of a cube with edge length $s$?

    $$V = s^{3}$$

  20. What is the general formula for the volume of any prism?

    $$V = B\,h$$ where $B$ is the area of the base and $h$ is the height (length perpendicular to the base).

  21. What is the formula for the volume of a cylinder?

    $$V = \pi r^{2} h$$ where $r$ is the base radius and $h$ is the height.

  22. What is the formula for the surface area of a rectangular solid (box) with dimensions $l$, $w$, $h$?

    $$SA = 2lw + 2lh + 2wh$$

  23. What is the surface area of a cube with edge length $s$, and why?

    $$SA = 6s^{2}$$ because a cube has 6 identical square faces, each of area $s^{2}$.

  24. What is a net of a three-dimensional solid?

    A net is a two-dimensional pattern that can be folded along its edges to form a 3-D solid; it shows all the faces flattened out.

  25. How many faces, edges, and vertices does a cube have?

    6 faces, 12 edges, and 8 vertices.

  26. List the equivalences for U.S. customary length: feet in a yard, inches in a foot, and feet in a mile.

    $1$ yard $= 3$ feet; $1$ foot $= 12$ inches; $1$ mile $= 5280$ feet.

  27. State the U.S. customary capacity conversions: cups in a pint, pints in a quart, and quarts in a gallon.

    $1$ pint $= 2$ cups; $1$ quart $= 2$ pints; $1$ gallon $= 4$ quarts.

  28. What do the metric prefixes kilo-, centi-, and milli- mean as factors of the base unit?

    kilo- $= 1000\times$; centi- $= \frac{1}{100}$ (0.01); milli- $= \frac{1}{1000}$ (0.001).

  29. How many meters are in a kilometer, centimeters in a meter, and millimeters in a meter?

    $1$ km $= 1000$ m; $1$ m $= 100$ cm; $1$ m $= 1000$ mm.

  30. To convert 2 hours and 45 minutes into total minutes, and what is the general method for elapsed time across an hour boundary?

    $2\times 60 + 45 = 165$ minutes. For elapsed time, convert to a common unit or count up to the next whole hour, then add the remaining time.

SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement FAQ

What is in the SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement syllabus?

SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement is split into 4 chapters: Lines, Angles, and Polygons, Perimeter, Area, and the Pythagorean Theorem, Solid Geometry and Volume and Measurement and Unit Conversion. Together they contain 17 topics and 8 sub-topics.

How many chapters are in SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement?

4 chapters, containing 17 topics and 8 sub-topics. The largest chapter is Perimeter, Area, and the Pythagorean Theorem, with 5 topics.

Are there flashcards for SSAT (Secondary School Admission Test) Quantitative Reasoning: Geometry and Measurement?

Yes — a 50-card Quantitative Reasoning: Geometry and Measurement deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.