MYP Geometry Unit 0 Building Blocks Review

Supplementary angles are two angles whose measures add up to 180°. Given one angle measures 112°, you can find the other angle by subtracting 112° from 180°. This calculation is 180° - 112° = 68°. Therefore, the measure of the other angle is 68°.

Complementary angles are two angles whose measures add up to 90°. Given that one angle measures 37°, to find the measure of the other angle, you subtract 37° from 90°. This calculation is: 90° - 37° = 53°. Therefore, the measure of the other angle is 53°.

In a triangle, the sum of all interior angles must equal 180°. Given the two angles measuring 45° and 85°, you can find the third angle by subtracting the sum of these two angles from 180°. First, add 45° and 85° to get 130°. Then, subtract 130° from 180°: 180° - 130° = 50°. Thus, the measure of the third angle is 50°.

Vertical angles are formed when two lines intersect, creating two pairs of opposite angles. By definition, vertical angles are always equal in measure, which means they are congruent. This property holds true regardless of the size or orientation of the intersecting lines. Thus, when two angles are vertical to each other, they will always have the same degree measurement, confirming their congruency.

When two parallel lines are intersected by a transversal, the alternate interior angles formed are equal in measure. This is a fundamental property of parallel lines and transversals, which states that alternate interior angles are congruent. This means that if one angle measures, for example, 50 degrees, the corresponding alternate interior angle will also measure 50 degrees, confirming their congruence. This property is crucial in various geometric proofs and applications.

When two parallel lines (r and s) are cut by a transversal, the co-interior angles on the same side of the transversal are supplementary, meaning they add up to 180°. Given one co-interior angle measures 110°, the other angle can be found by subtracting 110° from 180°. Thus, 180° - 110° equals 70°. Therefore, the measure of the other co-interior angle is 70°.

In an isosceles triangle, two sides are equal. Let NB = CN = x. The perimeter P is the sum of all sides: P = NB + CN + BC. Given P = 555 m and BC = 165 m, we can set up the equation: x + x + 165 = 555. Simplifying gives 2x + 165 = 555. Subtracting 165 from both sides results in 2x = 390, leading to x = 195 m. Thus, the length of NB is 195 m.

In Euclidean geometry, the sum of the interior angles of a triangle is always 180°. This can be demonstrated by drawing a line parallel to one side of the triangle and using alternate interior angles to show that the angles within the triangle add up to a straight line, which measures 180°. This fundamental property holds true for all triangles, regardless of their type or size, making it a key principle in geometry.

Lines that never intersect and remain equidistant from each other in the same plane are referred to as parallel lines. This means that no matter how far they are extended, they will never meet, maintaining a constant distance apart. Parallel lines are a fundamental concept in geometry, often used in various applications, including architecture and engineering, to create structures that require consistent spacing.

An isosceles triangle is defined by having two sides that are of equal length, known as congruent sides. This property distinguishes it from other types of triangles, such as scalene triangles, which have all sides of different lengths. The congruence of these two sides leads to equal angles opposite to them, further characterizing the triangle's geometric properties. Thus, the term "congruent" accurately describes the relationship between the two equal sides of an isosceles triangle.

Supplementary angles are defined as two angles whose measures add up to 180 degrees. This property is fundamental in geometry and applies to any two angles, regardless of their individual measures. For instance, if one angle measures 70 degrees, its supplementary angle would measure 110 degrees, since 70 + 110 = 180. This relationship is crucial in various geometric proofs and applications, making it a key concept in understanding angle relationships.

Alternate exterior angles formed by parallel lines cut by a transversal are actually equal, not supplementary. When two parallel lines are intersected by a transversal, the alternate exterior angles are congruent, meaning they have the same measure. Supplementary angles, on the other hand, sum up to 180 degrees. Therefore, since alternate exterior angles are equal and not necessarily adding up to 180 degrees, the statement is false.