5272道题目5525 条题源记录 · 相同内容已合并
相似・全等与比例线段挑战
In the figure shown, \( WZ \) and \( XY \) intersect at point Q, YQ = 36, WQ = 90, WX = 70, and XQ = 120. What is the length of \( YZ \) ?
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相似・全等与比例线段进阶
Rectangles \( ABCD \) and \( EFGH \) are similar. The length of each side of rectangle \( EFGH \) is 7 times the length of the corresponding side of rectangle \( ABCD \). The area of rectangle \( ABCD \) is 68 square units. What is the area of rectangle \( EFGH \), in square units?
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相似・全等与比例线段进阶
Triangle \( PQR \) is similar to triangle \( STU \), where \( P \), \( Q \), and \( R \) correspond to \( S \), \( T \), and \( U \), respectively. In triangle \( PQR \), the length of \( PQ \) is 6 and the length of \( QR \) is 24. In triangle \( STU \), the length of \( ST \) is 8. What is the length of \( TU \)?
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相似・全等与比例线段进阶
For the triangles shown, triangle ABC is dilated by a scale factor of 4 to obtain triangle XYZ, where d = 16. What is the measure, in degrees, of angle X?
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相似・全等与比例线段进阶
Rectangles \( ABCD \) and \( EFGH \) are similar. The length of each side of \( EFGH \) is 8 times the length of the corresponding side of \( ABCD \). The area of \( ABCD \) is 48 square units. What is the area, in square units, of \( EFGH \) ?
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相似・全等与比例线段进阶
In triangle DEF, the measure of angle D is 40° and the measure of angle E is 95°. In triangle RST, the measure of angle R is 40° and the measure of angle S is 95°. Which of the following additional pieces of information is needed to determine whether triangle DEF is similar to triangle RST ?
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相似・全等与比例线段进阶
Parallelogram \( ABCD \) is similar to parallelogram \( PQRS \). The length of each side of parallelogram \( PQRS \) is 2 times the length of its corresponding side of parallelogram \( ABCD \). The area of parallelogram \( ABCD \) is 30 square centimeters. What is the area, in square centimeters, of parallelogram \( PQRS \)?
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相似・全等与比例线段进阶
The table gives the perimeters of similar triangles \( TUV \) and \( XYZ \), where \( TU \) corresponds to \( XY \). The length of \( TU \) is 16.
What is the length of \( XY \)?
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相似・全等与比例线段进阶
In the figure, \( LQ \) intersects \( MP \) at point \( R \), and \( LM \) is parallel to \( PQ \). The lengths of \( MR, \) \( LR \) , and \( RP \) are 9, 10, and 19, respectively. What is the length of \( LQ \)?
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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 \( \frac{4}{7} \) 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 8, what is the length of \( CF \)?
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相似・全等与比例线段挑战
A property owner wants to find the length x, in feet, across a pond as represented in the figure. \( PR \) intersects \( ST \) at point \( Q \) , and \( ∠PTQ \) is congruent to \( ∠RSQ \). The lengths represented by \( PQ \), \( TQ \), \( QS \), and \( RS \) were determined to be 4,200 feet, 8,400 feet, 1,400 feet, and 1,600 feet, respectively. What is the value of x?
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相似・全等与比例线段进阶
In triangle DEF, the measure of angle D is 46° and the measure of angle E is 104°. In triangle RST, the measure of angle R is 46° and the measure of angle S is 104°. Which of the following additional pieces of information is needed to determine whether triangle DEF is similar to triangle RST?
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