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Authoritative PPT Summary
"Determination of Similar Triangles" PPT Courseware 2
The two sides correspond to two triangles that are proportional and have equal angles ________. This determination method can be understood by analogy with the "SAS" in congruent triangles. The two conditions of this theorem involve angles and sides respectively, one of which is indispensable, and this angle The ______ angles on both sides must be proportional.
1. (3 points) As shown in the figure, the diagonals AC and BD of the quadrilateral ABCD intersect at point O, and this quadrilateral is divided into four triangles ①, ②, ③, and ④. If OA:OC=OB:OD, then the following conclusion must be correct ()
A． ① is similar to ②
B． ① is similar to ③
C. ① is similar to ④
D. ② is similar to ④
2. (3 points) As shown in the figure, given △ABC, then among the following four triangles, the one similar to △ABC is ()
【Error-prone Inventory】
[Example] As shown in the figure, in △ABC, D and E are AB, and the upper point of AC is AB=7.8, AD=3, AC=6, CE=2.1. Try to judge whether △ADE and △ABC are similar.
[Incorrect explanation] Because AC=AE+CE, and AC=6, CE=2.1, so AE=6-2.1=3.9. Since ADAB≠AEAC, △ADE and △ABC will not be similar.
[Error Cause Analysis] The wrong explanation ignores the understanding of "correspondence" in the determination method of similar triangles. In fact, the corresponding side of AD is AC, not AB, and the corresponding side of AE is AB, not AC.
【Integrated use】
17． (14 points) As shown in the figure, in △ABC, AB=8 cm, BC=16 cm, point P moves from point A along AB to B at a speed of 2 cm/s, point Q starts from point B and moves along BC Point C moves at a speed of 4 cm/s. If P and Q start from A and B respectively at the same time, after how many seconds will △PBQ be similar to △ABC?
17. Assume that △PBQ is similar to △ABC after t seconds (0＜t＜4). If △QBP∽△ABC, then BPBC=BQAB, that is, 8-2t16=4t8, the solution is t=45; if △QBP∽ △CBA, then BPAB=BQBC, that is, 8-2t8=4t16, the solution is t=2, so after 45 seconds or 2 seconds, △PBQ is similar to △ABC
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"Determination of Similar Triangles" PPT Courseware 3:
"Determination of Similar Triangles" PPT Courseware 3 1. Three sides correspond to two proportional triangles ________. When using this judgment method to prove that two triangles are similar, pay attention to the corresponding relationship. Generally speaking, the opposite sides of equal angles are ________ sides. 2. Right triangle...
"Determination of Similar Triangles" PPT courseware:
"Determination of Similar Triangles" PPT courseware 1. If the angles of two triangles are equal, then the two triangles ________. 2. It is a common method to prove that two triangles are similar through the equality of two angles. The key to its application is to find the ________ angle. Generally speaking...