As shown in the figure, in rectangle ABCD, ab = 16, BC = 8, fold the rectangle along AC, point d falls at point E, and CE and ab intersect at F, then AF=______ .
From the properties of folding, we can get △ AEC ≌ △ CBA ﹥ ACF = ∠ caf ﹥ AF = cf. in RT △ CFB, from Pythagorean theorem, we can get CB2 + BF2 = CF2, that is 82 + (16-af) 2 = af2, and AF = 10
RELATED INFORMATIONS
- 1. As shown in the figure, in rectangle ABCD, ab = 16, BC = 8, fold the rectangle along AC, point d falls at point E, CE and ab intersect at point F, (1) prove: AF = CF (2) find the length of AF
- 2. In rectangle ABCD, ab = 4, BC = 6, fold the rectangle along AC, point d falls at e, and CE and ab intersect with F, then AF length is AB is not = 4, it is = 8
- 3. In rectangle ABCD, ab = 10, BC = 8, fold the rectangle along AC, point d falls at point E, and CE and ab intersect at point F, then the length of AF is
- 4. As shown in the figure, fold the rectangular piece of paper ABCD along the diagonal AC, so that point B falls at point E. verify: EF = DF
- 5. As shown in the figure, e and F are the points on the diagonal AC and BD of rectangular ABCD, and AE = DF
- 6. As shown in the figure, the quadrilateral ABCD is a rectangle, ad = 3, ab = 4. Fold the rectangle along the line AC, point B falls at point E, and connect De, then the length of De is () A. 1B. 95C. 725D. 75
- 7. Quadrilateral ABCD is a rectangle, ab = 4cm, ad = 3cm, fold the rectangle along the straight line AC, and point B falls at e to connect de. what is the figure of quadrilateral aced? What's its area? What's its perimeter?
- 8. As shown in the figure, the quadrilateral ABCD is a rectangle, AB: ad = 4:3, fold the rectangle along the straight line AC, point B falls at point E, and connect De, then de: AC = 1___ .
- 9. In rectangle ABCD, ab = 10cm, ad = 3cm, fold the rectangle along the straight line AC, point B falls at point E, connect De, what is the figure of quadrilateral aced, and explain the reason And calculate its area
- 10. As shown in the figure, the quadrilateral ABCD is a rectangle, ab = 4AD = 3, fold the rectangle along the straight line AC, point B falls at point E, connect De, what is the figure of quadrilateral aced What about perimeter and area
- 11. It is known that in square ABCD, ∠ man = 45 ° and ∠ man rotates clockwise around point a, and its two sides intersect CB and DC (or their extension lines) at points m and N respectively. When ∠ man rotates around point a to BM = DN (as shown in Figure 1), it is easy to prove that BM + DN = Mn (1) When ∠ man rotates around point a to BM ≠ DN (as shown in Figure 2), what is the quantitative relationship among BM, DN and Mn? Write out the conjecture and prove it; (2) when ∠ man rotates around point a to the position as shown in Fig. 3, what is the quantitative relationship among line segments BM, DN and Mn? Please write your guess directly
- 12. In square ABCD, am intersects BC at m, an intersects DC at n. angle man is 45 degrees. Angle man rotates clockwise around a, and its two sides intersect CB and DC at m respectively In square ABCD, am intersects BC at point m, an intersects DC at point n. angle man is 45 degrees. Angle man rotates clockwise around point a, and its two sides intersect CB and DC at point m and N respectively. When angle man rotates around point a to BM = DN, it is easy to prove BM + DN = Mn. When angle man rotates around point a to BM not = DN, what is the relationship between them?
- 13. As shown in the figure, in the square ABCD with side length of 8, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB with G, intersect CD with H. if cm = 2, then GH=______ .
- 14. As shown in the figure, square ABCD, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB at point G, intersect CD at point h. given am = 10cm, find the length of GH
- 15. As shown in the figure, in the square ABCD with side length of 8, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB with G, intersect CD with H. if cm = 2, then GH=______ .
- 16. As shown in the figure, square ABCD, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB at point G, intersect CD at point h. given am = 10cm, find the length of GH
- 17. As shown in the figure, square ABCD, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB at point G, intersect CD at point h. given am = 10cm, find the length of GH
- 18. In the parallelogram ABCD, am is perpendicular to BC and an is perpendicular to CD. It is proved that am: ab = Mn: AC
- 19. In the parallelogram ABCD, am ⊥ BC, an ⊥ CD, m and N are perpendicular feet. If AB = 13, BM = 5 and MC = 9, the length of Mn is______ .
- 20. Parallelogram ABCD, ab = BC, ∠ B = 60 °, ACD = 60 °, M is the point on BC, n is the point on CD, ∠ amn = 60 ° asks the relation between AM and Mn