As shown in the figure, ab ‖ CD, BC ⊥ AB, if AB = 4cm, s △ ABC = 12cm2, find the height of AB edge in △ abd

As shown in the figure, ab ‖ CD, BC ⊥ AB, if AB = 4cm, s △ ABC = 12cm2, find the height of AB edge in △ abd

S △ ABC = 12ab · BC = 12 × 4 · BC = 12, the solution is BC = 6, ∵ ab ∥ CD, the distance from point d to ab side is equal to the length of BC, and the height of AB side is equal to 6cm

It is known that, as shown in the figure △ ABC, ab = AC, ad ⊥ BC, the perpendicular foot is point D, an is the bisector of ⊥ cam, CE ⊥ an, and the perpendicular foot is e
(1) try to explain: the quadrilateral adce is a rectangle; (2) when △ ABC satisfies what conditions, the quadrilateral adce is a square? And give the proof

1. Proof: because AB = AC, ad ⊥ BC,
So ∠ bad = ∠ CAD (three lines in one),
Because an bisects ∠ cam, ∠ BAC + ∠ cam = 180 degree,
Therefore, CAD + can = 180 ° / 2 = 90 °,
And because of CE ⊥ an,
So ad ∥ CE, ∠ ADC = ∠ CEA = ∠ DAE = 90 °,
Then ∠ DCE = 90 °,
So the quadrilateral adce is a rectangle
2. When △ ABC is an isosceles right triangle, the quadrilateral adce is a square
Proof: because △ ABC is an isosceles right triangle,
Then ∠ BAC = 90 °,
So ∠ DAC = 45 °,
And because the quadrilateral adce is a rectangle,
So ∠ ADC = 90 °,
So ∠ ACD = 45 °,
So ad = DC,
So the quadrilateral adce is a square

Known: as shown in the figure, in △ ABC, ab = AC, ad ⊥ BC, perpendicular foot is point D, an is the bisector of ⊥ cam, CE ⊥ an, perpendicular foot is point E, (1) prove: quadrilateral adce is a rectangle; (2) when △ ABC meets what conditions, quadrilateral adce is a square? The proof is given

(1) It is proved that: in △ ABC, ab = AC, ad ⊥ BC, ∧ bad = ∠ DAC, ∧ an is the bisector of △ ABC outer angle ∠ cam, ∧ Mae = ∠ CAE, ∧ DAE = ∠ DAC + ∠ CAE = 12 × 180 ° = 90 ° and ∧ ad ⊥ BC, CE ⊥ an, ∧ ADC = ∠ CEA = 90 ° and ∧ quadrilateral adce is rectangular. (2) when ∧ ABC satisfies ∠ BAC = 90 °, quadrilateral adce is a square ACB = ∠ B = 45 °, ∵ ad ⊥ BC, ∵ CAD = ∠ ACD = 45 °, ∵ DC = ad, ∵ quadrilateral adce is a rectangle, ∵ rectangular adce is a square. When ∠ BAC = 90 °, quadrilateral adce is a square

In △ ABC, ab = AC, point D is the midpoint of BC, an is the bisector of △ ABC outer angle ∠ cam, CE ⊥ an, the perpendicular foot is point E, proving that the quadrilateral adce is a moment
shape

It is proved that ∠ NAC = ∠ ACB can be obtained from the known conditions, so an / / DC ∠ Dan = ∠ AEC = 90 degrees
So ad / / EC, so the quadrilateral adce is a parallelogram because it has an angle of 90 degrees
So the quadrilateral adce is a moment