標題:
發問:
Prove that "If two triangles satisfy the condition, AAA, then they are similar triangle." 更新: How to define similar triangle? All the sides are in proportion iff they are similar triangle. Is the above statement an axioma?
最佳解答:
You can use the sin law to prove that. Sin Law tell us that in the triangle ABC, AB/sin C = BC/sin A = AC/sin C Let there is two triangle PQR and XYZ, and angle P=X, Q=Y and R=Z. In the triangle PQR,we have: PQ/sin R = QR/sin P = PR/sin Q..............(1) In the triangle XYZ, we have: XY/sin Z =YZ/sin X = XZ/sin Y....................(2) (1)/(2),we have: PQsinZ/XYsinR = QRsin X/YZsinP = PRsin Y/XZsin Q...........(3) since angle P=X, Q=Y and R=Z, sin P=sin X, sin Q=sin Y and sin R=sin Z..................(4) Put (4) into (3), we have: PQ/XY = QR/YZ = PR/XZ All the sides are in proportion, so triangle PQR is similar to triangle XYZ.
其他解答:
http://i207.photobucket.com/albums/bb173/kkkpopup/solution.gif This method is suitable to Form 3 students who are not expected to know Sine Law. Yes, "3 sides proportional as well as equiangular" (both are true) is the definition of similar triangles.
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Prove the condition of similar triangle, AAA.發問:
Prove that "If two triangles satisfy the condition, AAA, then they are similar triangle." 更新: How to define similar triangle? All the sides are in proportion iff they are similar triangle. Is the above statement an axioma?
最佳解答:
You can use the sin law to prove that. Sin Law tell us that in the triangle ABC, AB/sin C = BC/sin A = AC/sin C Let there is two triangle PQR and XYZ, and angle P=X, Q=Y and R=Z. In the triangle PQR,we have: PQ/sin R = QR/sin P = PR/sin Q..............(1) In the triangle XYZ, we have: XY/sin Z =YZ/sin X = XZ/sin Y....................(2) (1)/(2),we have: PQsinZ/XYsinR = QRsin X/YZsinP = PRsin Y/XZsin Q...........(3) since angle P=X, Q=Y and R=Z, sin P=sin X, sin Q=sin Y and sin R=sin Z..................(4) Put (4) into (3), we have: PQ/XY = QR/YZ = PR/XZ All the sides are in proportion, so triangle PQR is similar to triangle XYZ.
其他解答:
http://i207.photobucket.com/albums/bb173/kkkpopup/solution.gif This method is suitable to Form 3 students who are not expected to know Sine Law. Yes, "3 sides proportional as well as equiangular" (both are true) is the definition of similar triangles.
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