What room Congruent Angles?

Congruent angles space two or more angles the are similar to one another (and to themselves). Congruent angles deserve to be acute, obtuse, exterior, or internal angles. That does not issue what type of edge you have; if the measure up of angle one is the exact same as angle two, they space congruent angles.

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Congruent in geometry way that one figure, even if it is it is (line segment, polygon, angle, or 3D shape), is the same to another in shape and also size. Equivalent angles top top congruent numbers are always congruent.

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Congruent angles Definition

The an interpretation of congruent angle is 2 or much more angles through equal procedures in levels or radians. Congruent angles require not challenge the same way or be created using the same figures (rays, lines, or heat segments). If the two angle dimensions are equal, the angles are congruent.

If angle B and also angle D have actually the same measure, castle are claimed to have congruency.


The easiest way to measure the variety of degrees in an angle is with a protractor.

Congruent angle Symbol

To talk and write around or attract angles, we need typical symbols and words to define them. We have three symbols mathematicians use:

≅ method one point is congruent to another∠ method an angle∡ is periodically used to show a measured angle°, as in 45°, method degreesrad means radians, a an approach of measuring angles in the metric system


Let"s look at at how we can define these 2 angles:


We can say that ∠O (angle O) and ∠A (angle A) are congruent, and also both measure 55°. We could likewise say the mathematically:

∠O ≅ ∠A∠O = ∠A = 55°

Since both angle measure less than 90°, castle are also acute and also are both made making use of rays. The shorthand description, ∠O and ∠A identifies each angle"s vertex, or point where light ray meet.

If you require the measure in radians, you will certainly write 0.959931 rad.

Reflexive residential property of Congruence

The Reflexive building of Congruence tells us that any kind of geometric number is congruent come itself. A heat segment, angle, polygon, circle, or another figure of the provided size and also shape is self-congruent.

Angles have a measurable level of openness, for this reason they have certain shapes and sizes. As such every edge is congruent come itself.

Congruent angles Examples

Angles can be oriented in any type of direction ~ above a aircraft and still be congruent. Simply as ∠DOG and also ∠CAT, above, were congruent yet were no “lined up” with each other, for this reason too deserve to congruent angles appear in any way on a page.

Here is a illustration that has actually several angles. I m sorry of this angles are congruent?:


All of this angles space congruent.

The direction — the way the 2 angles sit on the printed web page or display screen — is unimportant. The means the two angles are created is unimportant. If the actions in degrees or radians room equal, the angles space congruent.

Drawing Congruent Angles

You can attract congruent angles, or compare feasible existing congruent angles, making use of a illustration compass, a straightedge, and also a pencil.

One that the easiest ways to attract congruent angle is to draw two parallel lines cut by a transversal. In her drawing, the corresponding angles will be congruent. Girlfriend will have actually multiple pairs of angles with congruency.


Another easy method to draw congruent angles is to draw a best angle or a right triangle. Then, cut that right angle v an edge bisector. If you bisect the edge exactly, you room left to 2 congruent acute angles, every measuring 45°.


But what if you have a provided angle and also need to attract an identical (congruent) angle next to it:

Here room the steps for just how to draw congruent angles:

Draw a beam to the right of your initial angle, yet some street away. Produce an endpoint for your ray and also label it. Us will call ours Point M.Open your drawing compass so the the suggest on the compass have the right to be put on the peak of the currently angle, but the pencil does no reach previous the attracted line segment or beam of the currently angle.Without an altering the compass, ar the allude of the compass ~ above Point M ~ above your brand-new drawing. Swing an arc native Point M up into the room above your new ray.Move the compass allude to a point on one beam of the initial angle, then adjust the illustration compass, therefore the pencil touch the other point. Right here we put our compass ~ above Point K and also reach Point Y v it.Without changing the compass, move the compass allude to the brand-new ray"s point, here Point U, and also swing the arc the intersects with your original arc.Use your straightedge to connect the vertex, below Point M, through the intersection that the 2 arcs. Friend have duplicated the present angle.

If you need to compare two angles that space not labeled v their degrees or radians, friend can likewise use a illustration compass to find points on both angles and also measure their degree of openness.

If you do not have actually a protractor handy, you have the right to use found objects to get a feeling of an angle"s measurement. The square edge of a sheet of paper is 90°. If you wrinkles that edge over for this reason the two sides exactly line up, you have actually a 45° angle.

The place or orientation of two angles has actually nothing to execute with their congruence. Angles can be congruent while facing in two different directions.

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Congruent angles Word Problems

Suppose you are told that 2 angles the two different triangles space congruent. Does that average the triangles have to be congruent?One angle actions 91° and also is created of 2 rays. An additional angle measures 91° however is constructed of 2 line segments. Room the two angles congruent?Two angles space each 47°, yet one is do from a line and ray, the other is do from a line segment and a line. Are the two angles congruent?An angle procedures 1.8 rad. Is the angle congruent to anything?

Just as any angle is true to itself by gift congruent, be true to you yourself by act the occupational first, prior to checking the end the answers!

Two angle of two various triangles have the right to be congruent, yet that does not typical you have actually congruent triangles; they can be different sizes, and also their various other angles might have various measures.The 2 angles, one measure 91° and also constructed of two rays and also the other, also measuring 91° however constructed of 2 line segments, room congruent. Just the angle matters.Two angles, every measuring 47°, space congruent, no matter how they room constructed.An edge measuring 1.8 rad is congruent come itself.

What you learned:

After working your way through this lesson and also video, you have learned:

Congruent angles DefinitionHow to suggest congruent angles making use of symbolsFind congruent anglesThe reflexive home of congruence