Task Sets: Use informal arguments to establish facts about angles and similarity of triangles - Common Core Math - Grade 8

Recall / Warm-Up

These problems review skills you already know.

$Two parallel lines cut by a transversal, with the four angles at the top intersection numbered 1 to 4 and the four at the bottom intersection numbered 5 to 8.$

In the diagram, two parallel lines are cut by a transversal. Angle 1 and angle 5 are in the same position at each intersection. What is this pair of angles called?

Corresponding angles

Alternate interior angles

Co-interior angles

Vertical angles

Two angles are supplementary. One of them measures $130\degree$ . What is the measure of the other angle, in degrees?

From 8.G.A.4, two figures are similar when one can be obtained from the other by a sequence of rigid motions and a dilation. Which statement about similar triangles is true?

Corresponding angles are equal and corresponding sides are proportional.

Corresponding angles are equal and corresponding sides are equal.

All sides are equal but angles may differ.

The triangles must be exactly the same size.

Fluency Practice

Find each missing angle measure. State the relationship you used.

$Two parallel lines cut by a transversal, with the top-left angle at the upper intersection marked 62 degrees.$

Two parallel lines are cut by a transversal. One angle measures $62\degree$ . Find the measure of its corresponding angle at the other intersection, in degrees.

Two parallel lines are cut by a transversal. One interior angle measures $115\degree$ . What is the measure of the co-interior (same-side interior) angle?

$65\degree$

$115\degree$

$25\degree$

$90\degree$

$A triangle with bottom-left angle 38 degrees, bottom-right angle 74 degrees, and the top angle unknown.$

In a triangle, two of the interior angles measure $38\degree$ and $74\degree$ . Find the measure of the third interior angle, in degrees.

In triangle $ABC$ , angle $A = 40\degree$ and angle $B = 75\degree$ . In triangle $DEF$ , angle $D = 40\degree$ and angle $E = 75\degree$ . Are the triangles similar by the AA criterion?

Yes — two pairs of angles are equal, which is enough for AA similarity.

No — you must also check that the third pair of angles is equal.

No — you must also check that a pair of sides is equal.

There is not enough information to decide.

$A triangle with two interior angles 45 and 80 degrees, with one side extended to form an unknown exterior angle at the third vertex.$

In a triangle, two interior angles measure $45\degree$ and $80\degree$ . A side is extended at the third vertex to form an exterior angle there. Find the measure of that exterior angle, in degrees.

Use Informal Arguments to Establish Facts About Angles and Similarity of Triangles

Recall / Warm-Up

Fluency Practice