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

Quantitative Reasoning: Geometry and Measurement syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning: Geometry and Measurement in SSAT (Secondary School Admission Test), not a summary of it.

1. 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. 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. 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. 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

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

25 of 50 cards from the Quantitative Reasoning: Geometry and Measurement deck — real questions with worked 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?

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

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

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

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

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

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

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

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

    Add the lengths of all its sides.

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

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

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