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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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Quadrilaterals
- Properties of Quadrilateral
- 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
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
Theorem
Theorem: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
Proof: Let sides AB and CD of the quadrilateral ABCD be equal and also AD = BC in following fig.
Draw diagonal AC. Clearly, ∆ ABC ≅ ∆ CDA
So, ∠ BAC = ∠ DCA
and ∠ BCA = ∠ DAC
Hence ABCD is a parallelogram.
Shaalaa.com | Theorem: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
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