5272道题目5525 条题源记录 · 相同内容已合并
相似・全等与比例线段进阶
Triangle ABC is similar to triangle XYZ, such that A, B, and C correspond to X, Y, and Z, respectively. The length of each side of triangle XYZ is 2 times the length of its corresponding side in triangle ABC. The measure of angle B is 17°. What is the measure of angle Y, in degrees?
原库参考解析
相似・全等与比例线段挑战
The table gives the areas and perimeters of two similar rectangles, where n is a constant.
What is the value of n?
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相似・全等与比例线段挑战
In isosceles triangle \( ABC \) sides \( AB \) and \( AC \) are congruent. Point D divides side \( BC \) such that the length of \( BD \) is \( \frac{2}{3} \) of the length of \( BC \). Point E lies on side \( AB \) and point F lies on side \( AC \) such that when segments \( DE \) and \( DF \) are drawn, angle \( BED \) is congruent to angle \( CFD \). If the length of \( BE \) is 12, what is the length of \( CF \)?
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相似・全等与比例线段挑战
Each side of equilateral triangle R is multiplied by a scale factor of k to create equilateral triangle U. The length of each side of triangle U is \( \frac{1}{31} \) greater than the length of each side of triangle R. Which of the following could be the value of k?
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相似・全等与比例线段进阶
Trapezoid CDEF is similar to trapezoid JKLM, such that C, D, E, and F correspond to J, K, L, and M, respectively. The length of each side of trapezoid JKLM is 4 times the length of its corresponding side in trapezoid CDEF. The measure of angle C is 42°. What is the measure of angle J?
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相似・全等与比例线段挑战
In triangle RST, angle T is a right angle, point L lies on \( RS \), point K lies on \( ST \), and \( LK \) is parallel to \( RT \). If the length of \( RT \) is 63 units, the length of \( LK \) is 21 units, and the area of triangle RST is 252 square units, what is the length of \( KT \), in units?
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相似・全等与比例线段进阶
In the figure shown, triangle \( CAE \) is similar to triangle \( CBD \). The measure of angle\( CBD \) is 57°, and \( AE=24(BD) \) . What is the measure of angle \( CAE \)?
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相似・全等与比例线段进阶
In triangle ABC, \( DE \) is parallel to \( AC \), BD = AD, BE = 9, and AC = 17. What is the length of \( BC \)?
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相似・全等与比例线段进阶
Triangles FGH and JKL are congruent. In triangle FGH, FG = 2GH, FG = 28, and FH = 29. In triangle JKL, JK = 2KL. What is the length of segment JL?
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相似・全等与比例线段挑战
The floor of a store has an area of 4,400 square feet. An architect creates a scale model of the floor of the store, where the length of each side of the model is \( \frac{1}{20} \) times the length of the corresponding side of the floor of the actual store. What is the area, in square feet, of the scale model?
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相似・全等与比例线段进阶
Triangles ABC and A'B'C' are shown. Triangle ABC is dilated by a scale factor of 3 to form triangle A'B'C'. If the length of \( AB \) is 15, what is the length of \( A'B' \)?
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相似・全等与比例线段挑战
In the figure shown, triangle CAE is similar to triangle CBD. The measure of angle CBD is 58°, and AE = 23(BD). What is the measure of angle CAE?
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