## Elements of Geometry and Trigonometry |

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Page 68

The altitude of a

The altitude of a

**parallelogram**is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the perpendicular ... Page 69

Let AB be the common base of D CF EDF CE the two

Let AB be the common base of D CF EDF CE the two

**parallelograms**ABCD , ABEF : and since they are supposed to have the same ... But if from the quadrilateral ABED , we take away the triangle ADF , there will remain the**parallelogram**ABEF ... Page 70

Hence these two

Hence these two

**parallelograms**ABCD , ABEF , which havẽ the same base and altitude , are equivalent Cor . Every**parallelogram**is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Page 74

74 444 / sec SE GEOMETRY . ti The area of any

74 444 / sec SE GEOMETRY . ti The area of any

**parallelogram**is equal to the product of its base by its altitude . PROPOSITION V. THEOREM . For , the**parallelogram**ABCD is equivalent F D to the rectangle ABEF , which has the same base AB ... Page 75

therefore , the trapezoid ABCD is equivalent to the

therefore , the trapezoid ABCD is equivalent to the

**parallelogram**ADKL , and is measured by EFX AL . But we have AL = DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole