Prove — Geometry, what it means and where it is taught

The statement you must arrive at. Always the last line.

Taught in Geometry.

Where it is taught

What uses it later

This idea is needed for:

Practise this idea

12 questions in the course bank use Prove, in Scatter Plots & Association, Bivariate Data & Correlation, How to Write a Proof, Triangle Congruence Proofs, Similarity & Proportionality, Coordinate Geometry Proofs. The first 8 are below; the rest are in those units.

Problem 1

As study time increases, test scores increase. This is

  1. a positive association
  2. a negative association
  3. no association
  4. a causal proof
Worked answer

a positive association

Up together means positive

Nothing here proves cause

Problem 2

A strong r between two observed variables proves

  1. nothing about cause
  2. that the first causes the second
  3. that the second causes the first
  4. that a third variable is involved
Worked answer

nothing about cause

Correlation measures how they move together

Cause needs a controlled experiment

Problem 3

What is always the first line of a two-column proof?

  1. The given
  2. What you are proving
  3. A definition
  4. A theorem
Worked answer

The given

The given is your starting material.

The prove statement is the last line.

Problem 4

CPCTC may be used

  1. only after proving two triangles congruent
  2. at any point in a proof
  3. to prove triangles congruent
  4. only in coordinate proofs
Worked answer

only after proving two triangles congruent

It is what congruence gives you.

Using it to prove congruence would be circular.

Problem 5

In a proof you want to show AD ≅ CD. What is usually the step before?

Worked answer

prove the triangles containing them are congruent

Prove △ ABD ≅ △ CBD.

Then CPCTC gives the segments.

Problem 6

Which combination does NOT prove congruence?

  1. SSA
  2. SSS
  3. ASA
  4. AAS
Worked answer

SSA

SSA can give two different triangles.

It proves nothing.

Problem 7

Two pairs of congruent angles prove two triangles

  1. similar
  2. congruent
  3. isosceles
  4. right-angled
Worked answer

similar

The third angle follows, so all three match.

Same shape, any size: similar.

Problem 8

Two pairs of sides in ratio with the included angles congruent proves

  1. SAS similarity
  2. SSS similarity
  3. AA similarity
  4. congruence
Worked answer

SAS similarity

Two sides in ratio plus the angle between them.

That is SAS similarity.

Elsewhere

Browse all courses