"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 5

Description

"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 5

teaching objectives:

1. Further master the properties and determination theorem of rectangles.

2. Proficient in using property theorem and decision theorem to solve problems.

Teaching focus: Proof and comprehensive application of the determination theorem of rectangles.

Teaching difficulty: flexible application of rectangular judgment.

Known: As shown in the figure, in △ABC, AB=AC, AD is an angle bisector of △ABC, AN is the bisector of the exterior angle ∠CAM of △ABC, CE⊥AN, and the vertical foot is point E. Join DE and intersect AC at point F.

(1) Determine the shape of the quadrilateral ABDE and prove your conclusion;

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

1. It is known that among the following propositions:

(1) The rectangle is an axially symmetrical figure and has two axes of symmetry;

(2) A quadrilateral with two equal diagonals is a rectangle;

(3) A parallelogram with two equal angles is a rectangle;

(4) A quadrilateral with two equal diagonals that bisect each other is a rectangle. The correct ones are ()

A. 4 B. 3 C． 2 D． 1

2. As shown in the figure, in △ABC, the perpendicular bisectors of AC intersect AC and AB at points D and F respectively, and BE⊥DF intersects the extension line of DF at point E. It is known that ∠A=30°, BC=2, AF =BF, then the area of ​​quadrilateral BCDE is ____.

3. As shown in the figure, in △ABC, AB=6, AC=8, BC=10, P is a moving point on edge BC (and point P does not coincide with points B and C), PE⊥AB is in E, PF⊥ AC to F. Then the minimum value of EF is ()

A. 4B. 4.8 C. 5.2D． 6

4. As shown in the figure, O is the intersection point of rhombus ABCD diagonal AC and BD, CD=5cm, OD=3cm; passing through point C is CE∥DB, passing through point B is BE∥AC, CE and BE intersect at point E.

(1) Find the length of OC;

(2) Verify: the quadrilateral OBEC is a rectangle;

(3) Find the area of ​​rectangle OBEC.

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Update Time: 2024-09-08

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