In rectangular trapezoid ABCD, AD / / BC, ∠ ABC = 90 °, de ⊥ AC at point G, intersects the extension point e of AB, and AE = AC, if ad = DC = 2, find the length of DF How to prove that the DAC is 30 degree
It is proved that in triangle AED and triangle CED, ad = DC, angle AEB = angle CDE, ed = ed, then: Triangle AED and triangle CED are congruent. Then: AE = EC, AE = AC, AE = EC = AC, angle BAC = 60, angle BAE = 90, then: angle DCA = angle DAC = 30, AD / / BC, then: angle ACB = angle DCA = 30, and: de ⊥ AC is equal to
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- 1. As shown in the figure, in the trapezoidal ABCD, DC ‖ AB, ad = BC, BD bisects ∠ ABC, a = 60 ° (1) find the degree of ∠ abd; (2) if ad = 2, find the length of diagonal BD
- 2. It is known that in trapezoidal ABCD, DC | AB, ad = BC, BD bisects | ABC, | a = 60 degree Find the degree of ∠ abd If ad = 2, find the length of diagonal BD
- 3. As shown in the figure, it is known that in trapezoidal ABCD, ad is parallel to BC, ∠ ABC = 60 °, BD bisects ∠ ABC, and BD is vertical to DC (1) Verification: trapezoid ABCD is isosceles trapezoid (2) When CD = 1, find the circumference of the isosceles trapezoid ABCD
- 4. It is known that the bottom surface of the pyramid p-abcd is a right angled trapezoid, ab ‖ DC, ∠ DAB = 90 °. Please see the following It is known that the bottom of p-abcd is a right angled trapezoid, ab ‖ DC, ∠ DAB = 90 °, PA ⊥ bottom ABCD, PA = ad = DC = 1 / 2, ab = 1, e and m are the midpoint of edge PD and PC respectively 1. Verification: AE ⊥ PCD 2. Find a point n on the line AB so that the PDA of Mn ‖ plane
- 5. As shown in the figure, in the parallelogram ABCD, ab = 4, ad = 6, ∠ ABC = 60 °, point P is a moving point on the ray ad, BP and AC intersect at point E, let AP = X 1. Find the length of AC. 2. If △ ABC and △ BCE are similar, find the value of X. 3. If △ ABC is an isosceles triangle, find the value of X
- 6. In parallelogram ABCD, P is a point outside ad, and AP is vertical to PC, BP is vertical to PD, so find parallelogram ABCD as rectangle
- 7. P is a point in the square ABCD, and AP = 2. Rotate △ APB clockwise 60 ° around a to get △ AP ′ B ′. (1) make the rotated figure; (2) try to find the perimeter and area of △ app ′
- 8. Point P is a point in the square ABCD, connecting PA, Pb and PC. rotate the triangle PAB 90 degrees clockwise around point B to the position of triangle p'cb Let AB be a and Pb be B (b)
- 9. As shown in the figure, point P is a point in square ABCD. Rotate △ ABP around point B and coincide with △ BCP '. If BP = 3, find the length of PP ′ De
- 10. For a point in the square ABCD, rotate △ ABP clockwise 90 ° around B to the position of △ CBE, if BP = A. calculate the area of the square with PE as the side length Write every step in detail Using Pythagorean theorem
- 11. The bottom of p-abcd is a rectangle, the side pad is an equilateral triangle, and the side pad ⊥ bottom ABCD, When the value of AD / AB is equal to, it can make Pb ⊥ AC? And the proof is given
- 12. In a pyramid p-abcd, planar pad ⊥ planar ABCD, ab ∥ CD, △ pad are equilateral triangles. It is known that BD = 2ad = 8, ab = 2dc = 4 √ 5 Let m be a point on PC, and prove that planar MBD ⊥ planar pad
- 13. As shown in the figure, EF is the two points AE parallel CF on the diagonal BD of the quadrilateral ABCD, AE = CF, be = DF to prove the congruent triangle CBF of the triangle ade
- 14. The vertex a of the square ABCD is in the shape ∠ EAF = 45 °, e, f is in the shape BC.CD Let EF be ah ⊥ EF in H. prove ah = ab
- 15. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
- 16. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
- 17. ABCD is a square, AE = 4, EF = 3, AF = 5, find the area of ABCD E is on BC, f is on CD
- 18. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
- 19. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
- 20. P is a moving point outside the rectangular ABCD, and satisfies the AP vertical CP BP.DP When point P changes, does the degree of angle BPD change? If not, calculate the degree of angle BPD; if not, calculate the range of change