Common Core · High school
HSG-CO.C.9
High school — Prove theorems about lines and angles.
High school — Prove theorems about lines and angles, including that when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.
The 3 skills that cover it
- Logic & ProofRead a conditional statement, write its converse, inverse and contrapositive, test a claim with a counterexample, and give the reason for every step of a proof.Read the lesson →
- Parallel Lines & TransversalsName the angle pairs a transversal makes with two lines, use them to find unknown angles when the lines are parallel, and use them backwards to prove that two lines are parallel.Read the lesson →
- Polygons & QuadrilateralsFind the angle sums of any polygon, use the properties of parallelograms, rectangles, rhombi, squares, trapezoids and kites, and classify a quadrilateral from what is known about it.Read the lesson →
What a student should be able to do
- Identify the hypothesis and conclusion of a conditional statement.
- Write the converse, inverse and contrapositive and decide which are true.
- Use a counterexample, the law of detachment and the law of syllogism to test reasoning.
- Justify each step of an algebraic or geometric proof with a definition, property, postulate or theorem.
- Name corresponding, alternate interior, alternate exterior and co-interior angle pairs.
- Find unknown angles when a transversal crosses two parallel lines.
- Decide from one angle pair whether two lines are parallel.
- Solve for a variable in an algebraic angle relationship and relate perpendicular lines to right angles.
- Find the interior and exterior angle sums of a polygon and each angle of a regular one.
- Use the side, angle and diagonal properties of a parallelogram to find unknowns.
- Apply the special properties of rectangles, rhombi, squares, trapezoids and kites.
- Classify a quadrilateral from a list of its properties, choosing the most specific name.