8.8.d

Angles & Triangles 8th Grade

Texas Essential Knowledge and Skills (TEKS): 8.8.d
use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

The sum of the measures of the angles of a triangle is 180°.

Example:

The following sets of angles could not be the measures of the three angles of a triangle.

28° + 64° + 98° = 190°

19° + 40° + 111° = 170°

This set of angles could be the measures of the three angles of a triangle.

40° + 64° + 76° = 180°

The measure of an exterior angle of a triangle is equal to the
sum of the two non-adjacent interior angles of the triangle.

Example:

The following pair of angles could not be the values of w and x.

55° + 85° = 140°

The following pairs of angles could be the values of w and x.

44° + 91° = 135°

46° + 89° = 135°

If two angles of one triangle are congruent to
two angles of another triangle, the triangles are similar.

Example:

Solve for the missing angle in each triangle.

Triangle EFG: 180° − 90° − 44° = 46°
Triangle XYZ: 180° − 90° − 45° = 45°

If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. These triangles are not similar.

Example:

Based on their angle measures, the triangles are similar.
The side lengths of similar figures are proportional.
Set up a proportion and solve for x.

\begin{array}{rcl} \frac{1.4 cm}{2.8 cm} & = & \frac{2.8 cm}{x} \\ 1.4 cm (x) & = & 2.8 cm (2.8 cm) \\ x & = & 5.6 cm \end{array}

A transversal is a line which intersects two or more other lines.

In the image [above], lines m and n are cut by transversal t.
When lines intersect, a variety of angles are formed. Many of these angles have names.

In the image above, angles 3 and 6, and angles 4 and 5 are alternate interior angles.
When the lines cut by a transversal are parallel lines, alternate interior angles are congruent.

In the image above, angles 1 and 8, and angles 2 and 7 are alternate exterior angles.
When the lines cut by a transversal are parallel lines, alternate exterior angles are congruent.

In the image above, the following pairs of angles are corresponding angles: 1 and 5, 3 and 7, 2 and 6, and 4 and 8.
When the lines cut by a transversal are parallel lines, corresponding angles are congruent.

In the image above, angles 3 and 5, and angles 4 and 6 are same side interior angles.
When the lines cut by a transversal are parallel lines, same side interior angles are supplementary.

In the image above, the following pairs of angles are vertical angles: 1 and 4, 2 and 3, 5 and 8, and 6 and 7. Vertical angles are congruent.

Angles & Triangles

Texas Essential Knowledge and Skills (TEKS): 8.8.d

use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Processing Request...