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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
Cosine theorem C & # 178; = A & # 178; + B & # 178; - 2abcosc
So 2abcosc = 3AB
cosC=3/2
Isn't that right
As shown in the figure, ab = AC, ad ⊥ BC at point D, ad = AE, AB bisects ∠ DAE and intersects de at point F. please write out three pairs of congruent triangles in the figure and select one pair to prove it
(1) (2) taking △ ADB ≌ ADC as an example, it is proved that ≌ ad ⊥ BC, ≌ ADB = ≌ ADC = 90 ° in RT ≌ ADB and RT △ ADC, ab = Acad = ad ≌ RT ≌ ADB ≌ RT △ ADC (HL)
Known: as shown in the figure, ab = AC, ad = AE, ∠ BAC = ∠ DAE, verification: BD = CE
It is proved that: in ∵ bad and △ CAE, ad = AE, bad = caeab = AC, bad = SAS and BD = EC
Known: as shown in the figure, ad = AE, ab = AC, ∠ DAE = ∠ BAC
It is proved that: in ∵ bad and △ CAE, ad = AE, bad = caeab = AC, bad = SAS and BD = EC
RELATED INFORMATIONS
- 1. AB = AC, < BAC = < DAE, ad = AE, BD = CE
- 2. It is known as ab = AC, ad = AE, BD = CE
- 3. Known: as shown in the figure, ad = AE, ab = AC, ∠ DAE = ∠ BAC
- 4. 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
- 5. 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=______ ．
- 6. 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
- 7. 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
- 8. If there is a point C on the line AB with a length of 16 cm, then the distance between the midpoint of AC and BC is
- 9. As shown in the figure, given that point C is the midpoint of line AB, point D is the midpoint of BC, ab = 10cm, find the length of AD
- 10. As shown in the figure, C is the midpoint of line AB and D is the midpoint of line AC. given that the sum of the lengths of all line segments in the figure is 23, the length of line AC is______ ．
- 11. 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
- 12. 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
- 13. As shown in the figure, in RT △ ABC, ab = AC, ∠ BAC = 90 °, ∠ 1 = ∠ 2, CE ⊥ BD is extended to E. verification: BD = 2ce
- 14. In the triangle ABC, ab = AC, D is a point on BC, and
- 15. 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
- 16. 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
- 17. As shown in the figure, in equilateral △ ABC, CD intersects be at point F, ∠ BFC = 120?: ad = CE
- 18. 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
- 19. In △ ABC, D and E are on the lines AB and AC respectively, ad = 2, BD = 5, EA = 4, EC = 10, Ed: BC=
- 20. 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