# Write a conjecture about all the inscribed angles that intercept the same arc

Need a worksheet on linear equations? Or, an overview of literary devices? We've scoured the web to find and link to the best resources available to help you get your homework done. We can use a few more theorems to find the measures of arcs and central angles of circles. It means land or earth measurement. What are the conjectures from Discovering Geometry? C-2 V…ertical Angles Conjecture - If two angles are vertical angles, then they are congruent have equal measures.

## SparkNotes: Geometry: Theorems: Theorems for Angles and Circles

C-3a Corresponding Angles Conjecture CA - If two parallel lines are cut by a transversal, then corresponding angles are congruent. C-3 Parallel Lines Conjecture - If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent.

C-4 Converse of the Parallel Lines Conjecture - If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel.

Chapter 3 C-5 Perpendicular Bisector Conjecture - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.

C-6 Converse of the Perpendicular Bisector Conjecture - If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. C-7 Shortest Distance Conjecture - The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.

C-8 Angle Bisector Conjecture - If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. C-9 Angle Bisector Concurrency Conjecture - The three angle bisectors of a triangle are concurrent meet at a point.

C Perpendicular Bisector Concurrency Conjecture - The three perpendicular bisectors of a triangle are concurrent. C Altitude Concurrency Conjecture - The three altitudes or the lines containing the altitudes of a triangle are concurrent. C Circumcenter Conjecture - The circumcenter of a triangle is equidistant from the vertices.

## From the SparkNotes Blog

C Incenter Conjecture - The incenter of a triangle is equidistant from the sides. C Median Concurrency Conjecture - The three medians of a triangle are concurrent. C Centroid Conjecture - The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.

C Center of Gravity Conjecture - The centroid of a triangle is the center of gravity of the triangular region. C Third Angle Conjecture - If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal in measure to the third angle in the other triangle.

C Isosceles Triangle Conjecture - If a triangle is isosceles, then its base angles are congruent. C Converse of the Isosceles Triangle Conjecture - If a triangle has two congruent angles, then it is an isosceles triangle.

C Triangle Inequality Conjecture - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. C Side-Angle Inequality Conjecture - In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

C Triangle Exterior Angle Conjecture - The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.The measure of an angle inscribed in a circle is one-half the measure of the intercepted arc. Inscribed Angles Intercepting Arcs Conjecture Inscribed angles that intercept the same arc are congruent.

The measure of an angle inscribed in a circle is one-half the measure of the central angle. Inscribed angles intercepting arcs conjecture Inscribed angles that intercept the same arc are congruent.

## Inscribed Angles That Intercept the Same Arc - Wolfram Demonstrations Project

Conjecture 2: In a circle, two inscribed angles with the same intercepted arc are congruent. angle ABC = angleADC Conjecture 3: Any angle inscribed in a semi-circle is a right angle.

Chord Properties LESSON CONDENSED Inscribed Angles Intercepting Arcs ConjectureInscribed angles that intercept the same arc are _____. Investigation 3: Angles Inscribed in a Semicircle In Lesson , you discovered the Inscribed Angle Conjecture.

inscribed angles that intercept the same arc/or congruent arcs, are congruent Angles Inscribed in a Semicircle Conjecture angles inscribed in a semicircle are right angles.

Measure of inscribed angle = ½ measure of the intercepted arc. Therefore, $$\overparen{XZ} = 2 \cdot 40^{o}= 80^{o}$$ Every single inscribed angle in the picture on the left has the exact same measure, since each inscribed angle intercepts the exact same arc, which is $$\overparen {AZ}$$. C Inscribed Angle Conjecture - The measure of an angle inscribed in a circle is one-half the measure of the central angle. C Inscribed Angles Intercepting Arcs Conjecture - Inscribed angles that intercept the same arc are congruent. Write all that you have learned about the inscribed angle theorem. The measure of the central angle is double the measure of any inscribed angle that intercepts the same arc. Inscribed angles that intercept the same arc are congruent.

Prove your conjecture. R O O R T S P U T V Notes on your desk A Chapter Circles Unit 1: Tangents, Arcs, and Chords If two inscribed angles intercept the same arc, then the angles are congruent.

Corollary 2 An angle inscribed in a semicircle is a right angle.

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