12 multiple-choice questions, progressively harder.
Why are the usual simultaneous shadow triangles similar?
Solution
Correct answer: D
The stated physical arrangement establishes two matching angle pairs, so AA applies. A right angle by itself would give only one pair.
How is the shadow length of a tree measured in this model?
Correct answer: B
Each modeled triangle uses its own vertical height and its own ground leg. Combining endpoints from different objects changes the triangle.
Before forming a dimensionless map scale ratio from centimeters and meters, what must you do?
Correct answer: A
A dimensionless ratio compares like units. For example, a centimeter length must be compared with the real length expressed in centimeters, not an unconverted meter count.
Which observer measurement matches object height in the horizontal-mirror model?
Correct answer: C
The modeled vertical segment runs from the observer’s foot to the eye. It is that eye-height segment which corresponds to the vertical object height.
What supplies the equal-angle reflection rule used in the mirror model?
Geometry uses the reflection rule as a model premise. It does not prove a physical law of light.
In the mirror setup, F is the observer foot, M the mirror, B the object base, E the eye and T the top. Which segment corresponds to FM?
AA pairs the two ground legs FM and MB. The slanted sight lines and vertical heights belong to different side pairs.
In the crossed survey, AT and CD are perpendicular to the straight bank AC. T,B,D and A,B,C are collinear. Which facts give AA for TAB and DCB?
The perpendiculars give a right-angle pair. The two intersecting lines give the second, vertical-angle pair at B.
A uniform map scale is 1:1500. With common units, what is drawing length divided by real length?
The scale states that one drawing unit represents fifteen hundred real units of the same kind.
For that same 1:1500 map, what factor maps a drawing length to its real length in common units?
Going from the drawing to the real object multiplies by 1500. Going from real to drawing uses the reciprocal.
A similar image has every corresponding length equal to 3/23/23/2 of the original. What is its perimeter relative to the original?
Each boundary side gains the same factor. Adding all the image sides therefore gives three halves of the original perimeter.
Why does the same length factor apply to perimeter?
If every corresponding edge is multiplied by k, their sum is also multiplied by k. The entire matched boundary must be included.
An important model assumption has not been checked. What is the accurate conclusion about the proposed measurement?
An unsupported assumption leaves a gap in the justification. The answer might coincide with a correct value in some realization, but the argument has not guaranteed it.
Reset this practice set?
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