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In the parallelogram ABCD, ab ∥ CD, ad ∥ BC, e and F are on AD and CD respectively, and CE = AF. CE and AF intersect at point P, and In the parallelogram ABCD, ab ∥ CD, ad ∥ BC, e and F are on AD and CD respectively, and CE = AF, CE and AF intersect at point P, and Pb bisection ∠ APC is proved
Connect AC, BD, the intersection point is O, then the angle OAM = angle OCN, Ao = Co, because: angle AOM = angle con, so: Triangle AOM ≌ triangle con similarly: Triangle Bon ≌ triangle DOM, because: Ao = Bo = co = do, angle AOB = angle cod, so: triangle AOB ≌ triangle cod congruent triangle area is equal s (abnm) = s (triangle AOM) +
RELATED INFORMATIONS
- 1. In square ABCD, f is the midpoint of AD, BF and AC intersect at point G, then the area ratio of triangle BGC to quadrilateral CGFD is
- 2. In square ABCD, f is the midpoint of AD, BF and AC intersect point G, then the area ratio of triangle BGC and quadrilateral CGFD is? How to write the correct procedure?
- 3. In rectangular ABCD, if f is the midpoint of AD and BF and AC intersect point G, the area ratio of triangular BGC to quadrilateral CGFD is
- 4. In square ABCD, f is the midpoint of AD, BF and AC intersect at point G, what is the area ratio of triangle BGC to quadrilateral CGFD
- 5. The rectangular ABCD with an area of 1.6m2 is made of 10 identical rectangular floor tiles (as shown in the figure). What is the perimeter of the rectangular ABCD?
- 6. Eight identical small rectangular tiles are assembled into a large rectangular floor to calculate the area of the large rectangular floor
- 7. As shown in the figure, the rectangular pattern with a width of 50cm is made up of 10 identical small rectangles. What are the length and width of each rectangle?
- 8. Use 8 identical rectangular floor tiles just to form a rectangular pattern with a width of 20 cm, so how many square centimeters is the area of each rectangular floor tile?
- 9. Judgment question: use 30 cm long and 20 cm wide rectangular floor tiles to lay a square floor tile. At least 600 such tiles should be used
- 10. A batch of rectangular floor tiles is 18 cm long and 12 cm wide. How many such tiles do you need to make a square?
- 11. If the bisectors of parallelogram ABCD, ab = 5, ad = 8, angles C and D intersect ad, BC and points E and f respectively, and AF is perpendicular to BC, the solution of CE is obtained
- 12. In the parallelogram ABCD, it is known that the bisector ce of ∠ BCD intersects ad at e, the bisector BG of angle ABC intersects CE at f and ad at g. the proof is AE = dg
- 13. In the parallelogram ABCD (Xining City, 2008), the bisector ce of angle BCD intersects the edge ad at E (Xining City, 2008) 23. As shown in Figure 10, it is known that in the parallelogram ABCD, the bisector ce of angle BCD intersects ad at e, the bisector BG of angle ABC intersects CE at F, and ad at g. verification: AE = DG
- 14. In the parallelogram ABCD, passing through point C makes CE ⊥ CD and intersects ad at point E, Next, If ad = 6, tanb = 4 / 3, AE = 1, let CP1 = x, s △ p1f1c1 = y, find y and X, find the functional relationship between X and y, and write out the value range of independent variable x
- 15. In the parallelogram ABCD, m and N are the midpoint of DC and BC respectively. The known vectors am = C and an = D are used to represent the vectors AB and AD
- 16. Given any parallelogram ABCD, e is the midpoint of AD, f is the midpoint of BC, the proof is: ab + DC = 2ef
- 17. As shown in the figure, in the pyramid s-abcd, the bottom surface ABCD is a parallelogram, the side SBC ⊥ the bottom surface ABCD, ∠ ABC = 45 °, SA = sb, proving that SA ⊥ BC
- 18. It is known that the area of parallelogram ABCD is s, and the area of triangle PAB and triangle PCD are S1 and S2 respectively If point P is outside the parallelogram ABCD, then S1 + S2 -- half s Please explain why
- 19. If the area of parallelogram ABCD is 100, then s △ PAB + s △ PCD =
- 20. The length of diagonal lines AC and BD of quadrilateral ABCD are m and N respectively. It can be proved that when AC ⊥ BD (as shown in Figure 1), the area of quadrilateral ABCD is s = 12mn. Then when the acute angle between AC and BD is θ (as shown in Figure 2), the area of quadrilateral ABCD is s = () A. 12mnB. 12mnsinθC. 12mncosθD. 12mntanθ