## What is theorem 3.8 in geometry?

Theorem 3.8: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

## What is the proof theorem?

In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

**Is it possible to prove that the backrest and footrest of the lounging beach chair are parallel?**

ANSWER: Sample answer: Yes; since the alternate exterior angles are congruent, the backrest and footrest are parallel.

**How do you prove converse theorems?**

Statement: If the length of a triangle is a, b and c and c2 = a2 + b2, then the triangle is a right-angle triangle. Proof: Construct another triangle, △EGF, such as AC = EG = b and BC = FG = a. Thus, △EGF is a right triangle. Hence, we can say that the converse of Pythagorean theorem also holds.

### What is a theorem example?

A result that has been proved to be true (using operations and facts that were already known). Example: The “Pythagoras Theorem” proved that a2 + b2 = c2 for a right angled triangle. Lots more!

### Who is the father of geometry?

Euclid

Euclid, The Father of Geometry.

**Is it possible to prove that the backrest and footrest?**

RECREATION Is it possible to prove that the backrest and footrest of the lounging beach chair are parallel? If so, explain how. If not, explain why not. SOLUTION: Sample answer: Yes; since the alternate exterior angles are congruent, the backrest and footrest are parallel.

**How do you prove that lines are parallel in a proof?**

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. Proof Ex.

## What is converse proof?

In mathematics, the converse of a theorem of the form P → Q will be Q → P. The converse may or may not be true, and even if true, the proof may be difficult. For example, the Four-vertex theorem was proved in 1912, but its converse was proved only in 1997.

## What is parallel lines theorem?

If interior angles on the same side of the transversal sum to 180, then lines are parallel. If Alternate Interior angles have equal measure, then lines are parallel.