"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 8

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"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 8

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1. As shown in Figure 1, the two diagonals of rectangle ABCD intersect at point O. It is known that ∠AOD= 120°, AB=2.5cm, then ∠DAO=_____, AC=_____cm, S rectangle ABCD=_____.

2. As shown in Figure 2, quadrilateral ABCD is a parallelogram. Adding a condition _______________ can make it a rectangle.

Example 3 As shown in Figure 1-14, in the rectangle ABCD, AD=6, the diagonals AC and BD intersect at point O, AE⊥BD, the vertical foot is E, ED=3BE. Find the length of AE.

Solution ∵ Quadrilateral ABCD is a rectangle,

∴AO=BO=DO= BD ​​(the diagonals of the rectangle are equal and bisect each other).

∠BAD=90° (all four parts of the rectangle are right angles).

∵ED=3BE, ∴BE=OE.

Also ∵ AE⊥BD, ∴AB=AO.

∴AB=AO=BO.

Example 4 As shown in Figure 1-15, in △ABC, AB=AC, AD is the bisector of ∠BAC, AN is the bisector of the exterior angle ∠CAM of △ABC, CE⊥AN, and the vertical foot is E. Verification: The quadrilateral ADCE is rectangle.

Prove: ∵AD bisects ∠BAC, AN bisects ∠CAM,

∴∠CAD=1/2∠BAC, ∠CAN=1/2∠CAM.

∴∠DAE=∠CAD+∠CAN

=1/2（∠BAC+∠CAM）

=1/2 ×180°

=90°.

In Example 4, if DE is connected, AC intersects at point F (Figure 1-16)

(1) Try to determine the shape of the quadrilateral ABDE and prove your conclusion.

(2) What is the relationship between line segments DF and AB? Please justify your conclusion.

Class summary

1. Talk about your gains.

2. Talk about your confusion.

3. Tell me your method.

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Update Time: 2024-11-13

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