Question

what happens to the perimeter of a triangle when it is scaled by a factor of 3?
a. it quadruples
b. it triples
c. it doubles
d. it remains the same

in cartography, sss similarity is used to:
a. create accurate maps
b. measure angles
c. find the height of mountains
d. draw straight lines

how is sss similarity useful in graphic design?
a. to draw triangles
b. to calculate the area of shapes
c. to scale objects proportionally
d. to measure angles

which pair of triangles is not similar by sss similarity?
a. triangles with sides 1, 1, 1 and 2, 2, 2
b. triangles with sides 2, 3, 4 and 4, 6, 8
c. triangles with sides 3, 4, 5 and 5, 6, 7
d. triangles with sides 3, 4, 5 and 6, 8, 10

why is it necessary to check all three side ratios in sss similarity?
a. to find the scale factor
b. to confirm proportionality
c. to prove congruence
d. to calculate the perimeter

which of the following ratios would not indicate sss similarity?
a. (\frac{1}{2},\frac{2}{4},\frac{3}{6})
b. (\frac{4}{6},\frac{8}{12},\frac{9}{18})
c. (\frac{5}{10},\frac{1}{12},\frac{8}{16})
d. (\frac{2}{4},\frac{3}{6},\frac{1}{10})

why is it important to maintain proportional relationships in architectural models?
a. to make the models look nice
b. to ensure models are small

Explanation:

First question:

Step1: Recall perimeter formula

Let the sides of the original triangle be \(a\), \(b\), \(c\). The original perimeter \(P = a + b + c\). After scaling by a factor of \(3\), the new sides are \(3a\), \(3b\), \(3c\). The new perimeter \(P'=3a + 3b+3c\).

Step2: Factor out 3

Using the distributive property \(P' = 3(a + b + c)\). Since \(P=a + b + c\), then \(P'=3P\). So the perimeter triples.

Second question:

Step1: Understand SSS similarity in cartography

SSS (Side - Side - Side) similarity is used to create accurate maps. Maps are scaled - down (or up) versions of real - world geographical areas. By ensuring that the ratios of corresponding sides (distances on the map and actual distances) are equal (using SSS similarity concepts), accurate maps are made. Measuring angles is more related to protractors or trigonometric methods in some cases, finding mountain heights may involve trigonometry (not directly SSS similarity in a simple sense), and drawing straight lines is a basic drawing operation not related to SSS similarity.

Third question:

Step1: Relate SSS similarity to graphic design

In graphic design, when scaling objects, we want to maintain the shape. SSS similarity (ensuring that the ratios of corresponding sides of shapes are equal) helps in scaling objects proportionally. Drawing triangles is a basic drawing task, calculating area is a different geometric operation (using formulas like \(A=\frac{1}{2}bh\) for triangles etc.), and measuring angles is a separate geometric measurement.

Fourth question:

Step1: Check SSS similarity ratios

For option a: \(\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\), similar by SSS.
For option b: \(\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{1}{2}\), similar by SSS.
For option c: \(\frac{3}{5}
eq\frac{4}{6}
eq\frac{5}{7}\), not similar by SSS.
For option d: \(\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}\), similar by SSS.

Fifth question:

Step1: Purpose of checking all three ratios in SSS

SSS similarity criterion states that if the ratios of the three pairs of corresponding sides of two triangles are equal, then the triangles are similar. Checking all three ratios confirms proportionality. Finding the scale factor is a by - product of checking the ratios, proving congruence is a more strict condition (\(SSS\) congruence when ratios \( = 1\)), and calculating the perimeter is a separate operation.

Sixth question:

Step1: Simplify ratios

For option a: \(\frac{1}{3},\frac{2}{6}=\frac{1}{3},\frac{3}{9}=\frac{1}{3}\), equal ratios.
For option b: \(\frac{4}{8}=\frac{1}{2},\frac{8}{16}=\frac{1}{2},\frac{9}{18}=\frac{1}{2}\), equal ratios.
For option c: \(\frac{5}{10}=\frac{1}{2},\frac{7}{14}=\frac{1}{2},\frac{8}{16}=\frac{1}{2}\), equal ratios.
For option d: \(\frac{2}{4}=\frac{1}{2},\frac{3}{8}
eq\frac{1}{2},\frac{1}{10}
eq\frac{1}{2}\), not equal ratios.

Seventh question:

Step1: Importance of proportional relationships in architectural models

Maintaining proportional relationships in architectural models is to ensure that the model is a scaled - down (or up) version of the actual building. It's not just about looking nice (aesthetic can be a part but the core is functionality and accuracy), and making models small is a result of scaling but the key is proportionality for accurate representation.

Answer:

1. b. It triples
2. a. Create accurate maps
3. c. To scale objects proportionally
4. c. Triangles with sides 3, 4, 5 and 5, 6, 7
5. b. To confirm proportionality
6. d. \(\frac{2}{4},\frac{3}{8},\frac{1}{10}\)
7. (No correct option fully explained in the given choices, but the main idea is for accurate representation which is related to proportionality for functionality and not just aesthetics or size. If we assume the closest is related to accurate representation which is a more in - depth concept than just "looking nice")