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The document provides 5 problems related to inequalities in triangles and asks for a short explanation of each. The problems cover topics like determining if two sides of a triangle are equal based on their measures, comparing angles made by a tool with its handle and work surface, determining which intersection is closer to a third point based on angle measures, finding possible distances between vertices of a triangle drawn inside a kitchen, and determining which hiker is farther from camp based on their routes.

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Charles Miguel F. Rala
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57 views3 pages

11

The document provides 5 problems related to inequalities in triangles and asks for a short explanation of each. The problems cover topics like determining if two sides of a triangle are equal based on their measures, comparing angles made by a tool with its handle and work surface, determining which intersection is closer to a third point based on angle measures, finding possible distances between vertices of a triangle drawn inside a kitchen, and determining which hiker is farther from camp based on their routes.

Uploaded by

Charles Miguel F. Rala
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Demonstrate your understanding of inequalities in triangles by providing a short and concise

explanation for each of the problems below. Each problem is worth 5 points. The rubric on how you
will be graded with your answer is attached in this task.

1. The feather-shaped leaf below is called a pinnatifid. In the figure, does x = y? Explain.

Answer: 
x=y
28+ 81 = 32 + 78
109 is not equal to 110 so therefore, no, x is not equal to y.

2. Egyptian carpenters used a tool called adze to smooth and shape wooden objects. Does ∠E, the
angle the copper blade makes with the handle, have a measure less than or greater than the
measure of ∠G, the angle the copper blade the makes with the work surface. Explain.

Answer:
Name two angles in ∆MAL that have measures less than 90. ∠MLC is a 90° exterior angle.
∠M and ∠A are its remote interior angles. By Theorem. 7–4, m∠MLC.

3. Two roads meet at an angle of 50° at point A. A third road from B to C makes an angle of 45°
with the road from A to C. Which intersection, A or B, is closer to C? Explain.
Answer:

The smallest side is the side opposite to smallest angle in the triangle.
∆ ABC = A + B + C = 180°
∠B = 180° - (50 + 45)
∠B = 85°
The
___ angle smallest is ∠C = 45°
AB is the smallest side.
Largest angle = 85 = ∠B
AC is the largest side.
Angle___
=∠C ___< ∠A___
< ∠B
Side AB < BC < AC
The point closer to C is B Since AC > BC.

4. Some kitchen planners design kitchens by drawing a triangle and placing an appliance at each
vertex. If the distance from the refrigerator to the sink is 6 feet and the distance from the sink
to the range is 5 feet, what are the possible distances between the refrigerator and the range?
Explain your answer.

Answer:
6+5>ft
ft < 6 = 5
ft = 11

6 + ft > 5
Ft < 6 – 5
Ft < 1

Ft + 5 > 6
Ft < 6 – 5
Ft < 1

The answer is 1 < x < 11. Because according to the theorem 3 The sum of the lengths of two
sides of a triangle must always be greater of the third side.

5. Two hikers start at the visitor center. The first hikes 4 miles due west, then turns 40° toward
south and hikes 1.8 miles. The second hikes 4 miles due east, then turns 52° toward north and
hikes 1.8 miles. Which hiker is farther from camp? Explain how you know. 

Answer:

We should take into consideration that 40° to south means 140° and 52° to east means 128°.

We have:
___≅ AD
AB ___
___ ___
BC ≅ DF
m/ABC < m/ADF
___≅ AF
So. AC ___(Hinge Theorem)
The first hiker is farther from the visitor center.

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