California High School Proficiency Examination (CHSPE) Mathematics: Geometry and Measurement Syllabus

Mathematics: 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 Mathematics: Geometry and Measurement in California High School Proficiency Examination (CHSPE), not a summary of it.

1. 1

   Geometric Figures and Properties

   4 topics

   • Lines and Angles
     • Complementary, supplementary, and vertical angles
     • Angles formed by parallel lines and a transversal
   • Triangles
     • Classifying by sides and angles
     • Angle sum and the Pythagorean theorem
   • Quadrilaterals and Polygons
     • Properties of squares, rectangles, and parallelograms
     • Interior angle relationships
   • Circles
     • Radius, diameter, and circumference
     • Area of a circle
2. 2

   Perimeter, Area, and Volume

   3 topics

   • Perimeter and Circumference
     • Perimeter of polygons
     • Circumference applications
   • Area of Plane Figures
     • Rectangles, triangles, and parallelograms
     • Composite figures
   • Surface Area and Volume of Solids
     • Prisms and cylinders
     • Pyramids, cones, and spheres
3. 3

   Measurement and Units

   3 topics

   • U.S. Customary and Metric Systems
     • Length, weight, and capacity units
     • Converting within a system
   • Unit Conversions Across Systems
     • Approximate customary-metric conversions
     • Time and rate conversions
   • Precision and Estimation in Measurement
     • Choosing appropriate units
     • Estimating measurements
4. 4

   Transformations and Similarity

   3 topics

   • Congruence and Similarity
     • Corresponding parts of similar figures
     • Using proportions with similar figures
   • Transformations
     • Translations, reflections, and rotations
     • Identifying lines of symmetry
   • Scale and Indirect Measurement
     • Scale drawings and models
     • Using similar triangles to find unknown lengths

Mathematics: Geometry and Measurement flashcards for California High School Proficiency Examination (CHSPE)

23 of 50 cards from the Mathematics: Geometry and Measurement deck — real questions with worked answers.

1. What is the difference between a line, a ray, and a line segment?

   A line extends infinitely in both directions; a ray has one endpoint and extends infinitely in one direction; a line segment has two endpoints and a fixed length.

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

   Two angles whose measures add up to 90 degrees.

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

   Two angles whose measures add up to 180 degrees.

4. What are vertical angles, and how do their measures compare?

   Vertical angles are the opposite angles formed when two lines intersect; they are always equal (congruent).

5. When a transversal crosses two parallel lines, what is true of alternate interior angles?

   They are congruent (equal in measure).

6. When a transversal crosses two parallel lines, what is true of corresponding angles?

   They are congruent (equal in measure).

7. How are acute, right, obtuse, and straight angles defined by their measures?

   Acute < 90°, right = 90°, obtuse between 90° and 180°, straight = 180°.

8. What is the sum of the interior angles of any triangle?

   180 degrees.

9. How are triangles classified by their sides?

   Equilateral (all 3 sides equal), isosceles (2 sides equal), and scalene (no sides equal).

10. How are triangles classified by their angles?

    Acute (all angles < 90°), right (one 90° angle), and obtuse (one angle > 90°).

11. State the Pythagorean Theorem and when it applies.

    For a right triangle, a² + b² = c², where c is the hypotenuse (side opposite the right angle) and a, b are the legs.

12. What is 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.

13. What does the Exterior Angle Theorem state for a triangle?

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

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

    360 degrees.

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

    (n − 2) × 180 degrees.

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

    [(n − 2) × 180] / n degrees.

17. What is the sum of the exterior angles (one per vertex) of any convex polygon?

    360 degrees, regardless of the number of sides.

18. How do a square, rectangle, rhombus, and parallelogram differ?

    A parallelogram has 2 pairs of parallel sides; a rectangle is a parallelogram with 4 right angles; a rhombus is a parallelogram with 4 equal sides; a square has both 4 right angles and 4 equal sides.

19. What defines a trapezoid (US definition)?

    A quadrilateral with exactly one pair of parallel sides.

20. What is the difference between the radius and the diameter of a circle?

    The radius is the distance from the center to the edge; the diameter passes through the center from edge to edge and equals twice the radius (d = 2r).

21. What is a chord of a circle?

    A line segment whose endpoints both lie on the circle. The diameter is the longest chord.

22. What is the difference between an arc and a sector of a circle?

    An arc is a portion of the circle's circumference; a sector is the pie-slice region bounded by two radii and the arc between them.

23. How many degrees are in a full circle, and what is a central angle?

    A full circle is 360 degrees; a central angle is an angle whose vertex is at the center of the circle.

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