What are Congruent Angles?

Congruent angles room two or more angles that are the same to one one more (and come themselves). Congruent angles have the right to be acute, obtuse, exterior, or inner angles. That does not matter what form of angle you have; if the measure up of angle one is the exact same as edge two, they are congruent angles.

You are watching: Two angles that have the same measure

Congruent in geometry method that one figure, whether it is (line segment, polygon, angle, or 3D shape), is the same to another in shape and also size. Corresponding angles ~ above congruent figures are always congruent.

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Congruent angles Definition

The an interpretation of congruent angles is 2 or more angles with equal actions in levels or radians. Congruent angles need not face the same means or be constructed using the same figures (rays, lines, or line segments). If the two angle measurements are equal, the angles room congruent.

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


The easiest means to measure up the number of degrees in an edge is with a protractor.

Congruent angle Symbol

To talk and also write about or draw angles, we need usual symbols and also words to describe them. We have actually three symbols mathematicians use:

≅ means one point is congruent to another∠ means an angle∡ is sometimes used to suggest a measure up angle°, as in 45°, method degreesrad method radians, a method of measuring angle in the metric system


Let"s look at exactly how we can explain these two angles:


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

∠O ≅ ∠A∠O = ∠A = 55°

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

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

Reflexive residential property of Congruence

The Reflexive home of Congruence tells us that any geometric figure is congruent to itself. A line segment, angle, polygon, circle, or another figure of the offered size and shape is self-congruent.

Angles have actually a measurable level of openness, therefore they have details shapes and sizes. As such every angle is congruent to itself.

Congruent angle Examples

Angles can be oriented in any type of direction top top a aircraft and still be congruent. Just as ∠DOG and also ∠CAT, above, to be congruent however were not “lined up” through each other, so too deserve to congruent angles appear in any method on a page.

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


All of this angles room congruent.

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

Drawing Congruent Angles

You can attract congruent angles, or compare possible existing congruent angles, using a illustration compass, a straightedge, and also a pencil.

One of the easiest means to attract congruent angle is to attract two parallel lines cut by a transversal. In her drawing, the equivalent angles will certainly be congruent. You will have multiple pairs of angles v congruency.


Another easy means to attract congruent angles is to draw a appropriate angle or a appropriate triangle. Then, reduced that ideal angle through an angle bisector. If girlfriend bisect the edge exactly, you room left to two congruent acute angles, every measuring 45°.


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

Here are the steps for just how to attract congruent angles:

Draw a ray to the right of your original angle, yet some street away. Produce an endpoint for your ray and label it. Us will speak to ours Point M.Open your illustration compass so the the point on the compass deserve to be placed on the peak of the currently angle, but the pencil does not reach past the drawn line segments or rays of the currently angle.Without an altering the compass, place the suggest of the compass ~ above Point M on your brand-new drawing. Swing an arc native Point M up right into the an are above your brand-new ray.Move the compass allude to a allude on one ray of the initial angle, then readjust the illustration compass, therefore the pencil touch the various other point. Below we put our compass ~ above Point K and reach Point Y v it.Without transforming the compass, relocate the compass allude to the new ray"s point, right here Point U, and also swing the arc that intersects v your initial arc.Use her straightedge to connect the vertex, below Point M, with the intersection that the two arcs. You have duplicated the present angle.

If you must compare 2 angles that are not labeled through their degrees or radians, you can likewise use a drawing compass to locate points on both angles and also measure their level of openness.

If you do not have actually a protractor handy, you can use found objects to gain a sense of one angle"s measurement. The square leaf of a sheet of record is 90°. If you fold that edge over therefore the 2 sides precisely line up, you have a 45° angle.

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

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Congruent angle Word Problems

Suppose you room told that two angles the two different triangles are congruent. Go that typical the triangles must be congruent?One angle procedures 91° and also is created of 2 rays. Another angle measures 91° but is created of 2 line segments. Space the two angles congruent?Two angles space each 47°, but one is do from a line and also ray, the various other is make from a heat segment and a line. Space the two angles congruent?An angle procedures 1.8 rad. Is the edge congruent to anything?

Just as any angle is true to itself by gift congruent, be true to yourself by doing the work-related first, before checking the end the answers!

Two angles of two different triangles deserve to be congruent, yet that go not median you have congruent triangles; they could be different sizes, and their various other angles might have different measures.The two angles, one measure up 91° and constructed of 2 rays and the other, also measuring 91° however constructed of two line segments, are congruent. Only the edge matters.Two angles, every measuring 47°, space congruent, no matter how they room constructed.An edge measuring 1.8 rad is congruent to itself.

What you learned:

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

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