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Applications of Similarity: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

Two vertical objects are measured simultaneously, but their shadows lie on surfaces with different unknown slopes. Is the usual height-over-shadow proportion guaranteed?

Answer choices for question 1 A No; a matching ground-angle pair has not been established B Yes; simultaneous measurements alone are enough C No; every possible numerical equality is impossible D Yes; every pair of shadows forms similar triangles
2

In a valid mirror setup, EF is eye height, TB object height, FM and MB are ground legs, and EM is a slanted sight line. Which proportion is supported?

Answer choices for question 2 A $\frac{TB}{EF}=\frac{MB}{EM}$ B $\frac{TB}{EF}=\frac{FM}{MB}$ C $\frac{TB}{EF}=\frac{MB}{FM}$ D $\frac{TB}{EF}=\frac{FB}{FM}$
3

In the crossed survey, A,B,C and T,B,D are collinear in order, while AT and CD are perpendicular to AC. Which ordered similarity states the correspondence correctly?

Answer choices for question 3 A $\triangle TAB\sim\triangle CDB$ B $\triangle TAB\sim\triangle DCB$ C $\triangle TAB\sim\triangle BCD$ D $\triangle TAB\sim\triangle DBC$
4

In a valid crossed survey, the ratio of bank segments AB:BC is 7:3 and accessible perpendicular CD is 4.20 m. Find inaccessible perpendicular AT.

Answer choices for question 4 A $1.80\text{ m}$ B $12.6\text{ m}$ C $29.4\text{ m}$ D $9.80\text{ m}$
5

A print changes a 4.0 cm horizontal length to 5.0 cm and a 9.0 cm vertical length to 10.8 cm. Can one new similarity scale describe the whole print?

Answer choices for question 5 A Yes; the horizontal factor alone is sufficient B Yes; the larger factor applies everywhere C No; the two directional factors differ D No print can ever preserve a scale
6

Two similar triangular frames have original and image perimeters 72 and 108 cm. Corresponding sides are 2x+4 and 5x-1 cm. Find x.

Answer choices for question 6 A $3.5$ B $2$ C $5$ D $7$
7

A measurement calculation gives 17.8625 m. The task asks for an estimate to the nearest tenth of a meter. Which report is appropriate?

Answer choices for question 7 A $\text{Exactly }17.862500\text{ m}$ B $\text{Approximately }17.8\text{ m}$ C $\text{Exactly }18\text{ m}$ D $\text{Approximately }17.9\text{ m}$
8

A 5 cm model edge corresponds to a 12 m real edge. What is the factor mapping real lengths to model lengths in common units?

Answer choices for question 8 A $240$ B $\frac 1{240}$ C $\frac 5{12}$ D $2.4$
9

A mirror is horizontal and the modeled triangles have right angles, but no reflection-angle relation is supplied. What further premise does the usual AA argument need?

Answer choices for question 9 A Equality of the two object heights B The physical equal-angle reflection rule C An inaccessible sight-line length measured directly D The fact that every pair of right triangles is similar
10

An original triangular boundary has sides a,b,c. A similar image has corresponding sides ka,kb,kc for positive k. Which perimeter equation is justified?

Answer choices for question 10 A $P_{\rm image}=k^2(a+b+c)$ B $P_{\rm image}=a+b+c+k$ C $P_{\rm image}=(a+b+c)/k$ D $P_{\rm image}=k(a+b+c)$
11

An original 1:6000 map is reprinted uniformly. The new print has scale 1:4000. What is new drawing length divided by old drawing length?

Answer choices for question 11 A $\frac 23$ B $2.5$ C $1.5$ D $\frac 16$
12

A simultaneous shadow check gives height/shadow ratios 2.4/1.8 and 4.0/3.0 for two calibration objects. What does their agreement show?

Answer choices for question 12 A The readings are consistent with a common ratio; agreement alone does not verify every model assumption B The physical assumptions have all been proved by one calculation C Every future measurement must be exact D The objects must have equal heights

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