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Chapter 5: Problem 12

A logo in an advertisement is an equilateral triangle with a side length of 7 centimeters. Sketch the logo and give the measure of each side.

Short Answer

Expert verified
The sides of the equilateral triangle logo measure 7, 7, and 7 centimeters respectively.

Step by step solution

01

Understand the concept of an equilateral triangle

An equilateral triangle has all equal sides. This means each side measures the exact same length.
02

Apply the properties of the equilateral triangle to the given problem

In this case, the side length of the equilateral triangle is given as 7 centimeters. It implies that every side of the equilateral triangle would measure 7 centimeters.
03

Sketch the triangle and indicate the side lengths

Draw an equilateral triangle on your paper. At each side, write '7 cm' to indicate the length of the side of the triangle. All sides should clearly be marked with '7 cm'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equilateral Triangle
An equilateral triangle is a special type of triangle where all three sides have the same length. This characteristic gives it a symmetrical appearance and results in equal angles, each measuring 60 degrees. Because the sides are equal, calculations involving perimeter and area can be simplified.
  • All sides are the same length.
  • All angles are equal and measure 60 degrees.
  • The symmetry aids in geometric proofs and understanding symmetrical properties.
Understanding equilateral triangles helps in not only identifying them but also in solving various geometrical problems. Their regularity makes them a fundamental shape in geometry.
Side Length
The side length of a shape is a fundamental concept that refers to the measure of one of its sides. For an equilateral triangle, the side length is uniform across all sides. In the given exercise, the side length is 7 centimeters, meaning:
  • Each side of the triangle is 7 cm long.
  • The total perimeter of the triangle is calculated as 21 cm (since there are 3 sides, each 7 cm long: \(3 \times 7 = 21\) cm).
Knowing the side length allows for further calculations, such as finding the area or determining other properties or features of the triangle. Consistency in side length ensures equal distribution of properties across the shape.
Properties of Triangles
Triangles, in the realm of geometry, possess several distinct properties that vary depending on the type of triangle. For equilateral triangles:
  • All sides and angles are equal, contributing to its regular shape.
  • The interior angles always sum up to 180 degrees.
  • They have rotational symmetry of order 3, meaning they look the same after a rotation of 120 degrees.
These properties are helpful in understanding geometric proofs and solving problems. Recognizing the properties of equilateral triangles aids students in predicting and verifying the outcomes of geometric calculations.
Sketching Geometric Shapes
Sketching geometric shapes such as triangles involves translating the properties and dimensions onto paper. To sketch an equilateral triangle:
  • Begin by drawing one side accurately to the given length, here 7 cm.
  • Use a compass or protractor to ensure the other sides are equal, forming the characteristic 60-degree angles.
  • Label each side with its length, so in this case, each side should be marked as '7 cm'.
Sketching aids in visualizing the geometric properties and provides a hands-on understanding of the shapes, enhancing the learning experience. It also serves as a foundational skill in more complex geometric and technical drawings.

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Most popular questions from this chapter

In Exercises \(23-26,\) ind the measure of each acute angle in the right triangle. The measure of one acute angle is twice the difference of the measure of the other acute angle and 12 .

In Exercises \(15-18,\) write a proof \(\begin{array}{ll}{\text { Given }} & {\overline{\mathrm{PT}} \cong \overline{\mathrm{RT}}, \overline{\mathrm{QT}} \cong \overline{\mathrm{ST}}} \\\ {\text { Prove }} & {\Delta \mathrm{PQT} \cong \triangle \mathrm{RST}}\end{array}\)

Find the coordinates of the midpoint of the line segment with the given endpoints. $$J(-2,3) \text { and } \mathrm{K}(4,-1)$$

MAKING AN ARGUMENT Your friend claims that in order to use the SSS Congruence Theorem (Theorem 5.8) to prove that two triangles are congruent, both triangles must be equilateral triangles. Is your friend correct? Explain your reasoning.

ANALYZING RELATIONSHIPS Which of the following could represent the measures of an exterior angle and two interior angles of a triangle? Select all that apply. A. \(100^{\circ}, 62^{\circ}, 38^{\circ}\) B. \(81^{\circ}, 57^{\circ}, 24^{\circ}\) C. \(119^{\circ}, 68^{\circ}, 49^{\circ}\) D. \(95^{\circ}, 85^{\circ}, 28^{\circ}\) E. \(92^{\circ}, 78^{\circ}, 68^{\circ}\) F. \(149^{\circ}, 101^{\circ}, 48^{\circ}\)
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