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As shown in the figure, in RT △ ABC, ab = AC, ∠ BAC = 90 °, ∠ 1 = ∠ 2, CE ⊥ BD is extended to E. verification: BD = 2ce
It is proved that: extend the intersection of CE and BA at point F, as shown in the figure, ∵ be ⊥ EC, ∵ bef = ∠ CEB = 90 °. ∵ BD bisection ∵ ABC, ∵ 1 = ∠ 2, ∵ f = ∠ BCF, ∵ BF = BC, ∵ be ⊥ CF, ∵ CE = 12CF, ∵ △ ABC, AC = AB, ∵ a = 90 °, ∵ CBA = 45 ° and ∵ f = (180-45) ° △ 2 = 67.5 °
As shown in the figure, it is known that ∠ BAC = 90 °, ab = AC, BD bisects ∠ ABC, intersects AC with D, and makes CE ⊥ BD with E. (1) explore the relationship between BD and EC (2)
Connecting AE to calculate ∠ AEB degree
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Extending the intersection of CE and BA at F1, ∵ BAC = 90 ∵ CAF = 90 ∵ BAC = 90, ∵ abd + ≌ ADB = 90 ∵ CE ⊥ BD ∵ ACF + CDE = 90 ∵ ADB = CDE ∵ abd = ACF ≌ AB = AC ≌ abd ≌ ACF (ASA) ∵ BD = CF ≌ ABC, CE ⊥ BD ≌ CE = EF = CF / 2 (three
The length of two sides of a right triangle is 8 cm and 6 cm respectively. The volume of the newly formed cone is much larger when it rotates around the axis of the straight line where the longer right side is located
Radius = 6 cm
H = 8 cm
Volume = 1 / 3 × 3.14 × 6 & # 178; × 8 = 301.44 cm3
If the right triangle in the question above is rotated around the right side of 8 cm to form a cone. What is the circumference of the bottom surface of the cone? What is the height of the cone?
Turn the right triangle in the figure below around the right side of 6cm to form a cone. What's the circumference of the bottom of the cone? What's the height? It's 6cm vertically and 8cm horizontally,
1. Take the right angle side of 6cm as the axis
The circumference of the base of the cone is 2 π r = 2 π * 8 = 16 π (CM)
The height of the cone is 6 cm
2. Take the right angle side of 8 cm as the axis
The circumference of the base of the cone is 2 π r = 2 π * 6 = 12 π (CM)
The height of the cone is 8 cm
RELATED INFORMATIONS
- 1. As shown in the figure, in the triangle ABC, the angle ACB = 90 °, CD is perpendicular to AB, the perpendicular foot is D, and the angle a = 60 ° to prove BD = 3aD
- 2. As shown in the figure, in the triangle ABC, the angle ACB is 90 degrees, the angle CD is high, and the angle a is 30 degrees
- 3. In the triangle ABC, we know that the opposite sides of angles a, B and C are a, B and C respectively, and a * a + b * B-C * C = / 3A * B. find the size of angle A
- 4. AB = AC, < BAC = < DAE, ad = AE, BD = CE
- 5. It is known as ab = AC, ad = AE, BD = CE
- 6. Known: as shown in the figure, ad = AE, ab = AC, ∠ DAE = ∠ BAC
- 7. In triangle ABC, D is on AB, CD bisector angle ACB, if CB equals a, CA equals B, find CD The RT process is detailed CA doesn't equal CB. Notice
- 8. Given that the line segment AB = 10cm, there is a point C on the line AB, and BC = 2cm, M is the midpoint of the line segment AC, then am=______ ．
- 9. If M is the midpoint of AC and N is the midpoint of BC, then the length of segment Mn is () A. 7cmb. 3cmc. 7cm or 3cmd. 5cm
- 10. As shown in the figure, line AB = 16cm, C is the point on AB, BC = 10cm, D is the midpoint of line AC, find the length of DB
- 11. In the triangle ABC, ab = AC, D is a point on BC, and
- 12. As shown in the figure, it is known that CD is perpendicular to ab at point D, be is perpendicular to AC at point E, and CD intersects be at point o (1) If OC = ob, prove that point O is on the bisector of angular BAC (2) If point O is on the bisector of angle BAC, OC = ob is proved
- 13. In 3-angle ABC, the angle BAC is 90 degrees, ad is perpendicular to BC, EF is perpendicular to BC, FM is perpendicular to AC, the perpendicular foot is D, F, m respectively, angle 1 = angle 2, verification: FM = FD
- 14. As shown in the figure, in equilateral △ ABC, CD intersects be at point F, ∠ BFC = 120?: ad = CE
- 15. It is known that CD is the height of AB side in △ ABC, AC + BC = 8, CD = 2, AE is the diameter of circumscribed circle of △ ABC, (1) try to explain △ CBD ∽ AEC, (2) let AC = x, AE = y, find the functional relation of y with respect to x, and (3) find the maximum value of Y
- 16. In △ ABC, D and E are on the lines AB and AC respectively, ad = 2, BD = 5, EA = 4, EC = 10, Ed: BC=
- 17. It is known that: as shown in the figure, the circle O with the diameter of AB on one side of the equilateral triangle ABC intersects with the sides AC and BC at points D and e respectively, DF ⊥ BC is made through point D, and F is the perpendicular foot (1) Proof: DF is tangent of circle O (2) If the side length of equilateral triangle ABC is 4, find the length of DF (3) Finding the area of the shadow in a graph The first question is not, the shadow area is DFE
- 18. If the square of a plus the square of B equals twice the square of C, then the minimum value of COSC is
- 19. In the triangle ABC, a = 120 °, ab = 5, BC = 7, then the value of sina / SINB
- 20. In the right triangle ABC, C is equal to 90 degrees, AC is equal to twice BC, then the value of sina is?