Geometry Vocabulary Unit-4 Flashcards

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Questions and Answers

What is an equiangular triangle?

A triangle with two equal sides

A triangle with no equal sides

A triangle where all angles are equal (correct)

A triangle where all sides are equal

What defines an equilateral triangle?

All sides are equal (correct)

All angles are equal (correct)

Two sides are equal

None of the above

How many sides does an isosceles triangle have?

Three (correct)

One

Two

Four

What is meant by the term 'legs' in a triangle?

The legs of a triangle refer to its sides, specifically in a right triangle, the sides other than the hypotenuse. Signup and view all the answers

Define a right triangle.

A right triangle is a triangle in which one angle is a right angle (90 degrees). Signup and view all the answers

What is the Triangle Inequality Theorem?

The sum of any two sides of a triangle must be greater than the third side Signup and view all the answers

What is a scalene triangle?

A scalene triangle is a triangle with all three sides of different lengths. Signup and view all the answers

Explain the Exterior Angle Theorem.

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of its remote interior angles. Signup and view all the answers

What is the definition of congruent polygons?

Congruent polygons are two polygons that are the same size and shape, with corresponding angles and sides being equal. Signup and view all the answers

What is the definition of altitude in a triangle?

An altitude of a triangle is a line segment from a vertex perpendicular to the line containing the base. Signup and view all the answers

Define centroid.

The centroid of a triangle is the point where the three medians intersect. Signup and view all the answers

What is a hypotenuse?

The hypotenuse is the longest side of a right triangle, opposite the right angle. Signup and view all the answers

What does AAS postulate stand for?

Angle-Angle-Side postulate. Signup and view all the answers

What is the Scale Factor?

The scale factor is the ratio of any two corresponding lengths in two similar geometric figures. Signup and view all the answers

Describe the Area in geometry.

Area is the measure of space inside the boundary of a 2-dimensional object, like a triangle or circle. Signup and view all the answers

What does the Perpendicular Bisector Theorem state?

The locus of all points equidistant from the endpoints of a segment Signup and view all the answers

What is the SSS postulate?

If three sides of one triangle are equal to three sides of another, the triangles are congruent Signup and view all the answers

Study Notes

Triangle Types and Properties

Equiangular Triangle: All three interior angles measure 60°, thus it is also an equilateral triangle.
Equilateral Triangle: All three sides are equal, leading to congruent internal angles of 60°.
Isosceles Triangle: Has at least two sides of equal length; includes equilateral triangles as a special case.
Scalene Triangle: All sides are of different lengths, resulting in three unequal angles.
Right Triangle: Contains one 90-degree angle; the side opposite this angle is the hypotenuse.

Triangle Parts and Theorems

Legs: Sides of a triangle, specifically in right triangles, legs are the two sides forming the right angle; the hypotenuse is the longest side.
Base: In an isosceles triangle, it refers to the unequal side; the altitude is the perpendicular distance from the base to the vertex.
Exterior Angle Theorem: The measure of an exterior angle is greater than either of the remote interior angles. This theorem does not rely on the parallel postulate.
Triangle Inequality Theorem: The sum of any two sides must be greater than the third side.

Special Triangle Angles

Base Angles: In an isosceles triangle, the two angles opposite the base are equal.
Vertex Angle: The angle opposite the base in an isosceles triangle; examples include its measurement as seen in triangle properties.

Congruence Postulates

AAS Postulate: If two angles and a non-included side of one triangle are congruent to two angles and the non-included side of another triangle, the triangles are congruent.
ASA Postulate: If two angles and the included side are congruent between two triangles, then the triangles are congruent.
SAS Postulate: If two sides and the included angle are congruent between two triangles, the triangles are congruent.
SSS Postulate: If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
HL Theorem: In right triangles, if the hypotenuse and a leg are congruent, then the triangles are congruent.

Triangle Centers and Properties

Centroid: The intersection point of the three medians of a triangle, also known as the center of gravity.
Circumcenter: The intersection point of the perpendicular bisectors of the sides; it is the center of the circumcircle.
Median: A segment connecting a vertex to the midpoint of the opposite side; each triangle has three medians.

Mid-segment and Geometric Concepts

Mid-segment: Connects midpoints of two sides of a triangle; it is parallel to the third side and half its length.
Altitude: A perpendicular line segment from a vertex to the line containing the base.
Perpendicular Bisector: The locus of points equidistant from the endpoints of a segment.

Geometrical Relations and Calculations

Proportion: A relationship between two quantities being equal in ratios, such as comparing lengths.
Ratio: Indicates how many times one number contains another, e.g., the ratio of oranges to lemons.
Scale Drawing: A representation where the lengths are proportionally reduced or enlarged.
Volume: Measures the space within a 3D object, expressed in cubic units.

Additional Geometrical Theorems

Side-Splitter Theorem: States that a line parallel to one side of a triangle divides the other two sides proportionally.
Corollary: A statement that is derived easily from a theorem.

Conclusion

Understanding triangle properties, types, and congruence is fundamental in geometry, laying the groundwork for complex applications and proofs.

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Description

Test your knowledge of key terms in geometry with these flashcards from Vocabulary Unit 4. This set covers important concepts such as equiangular and equilateral triangles, helping you master essential definitions and their properties. Perfect for students looking to reinforce their understanding of geometry terms.