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Introduction to Euclid’S Geometry
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Lines and Angles
- Introduction to Lines and Angles
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- Introduction to Parallel Lines
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- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles
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Quadrilaterals
- Concept of Quadrilaterals
- Properties of a Quadrilateral
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- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
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Theorem
Theorem: A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.
In above fig. which is AB = CD and AB || CD . Let us draw a diagonal AC. You can show that ∆ ABC ≅ ∆ CDA by SAS congruence rule. So , BC || AD .
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