When two lines intersect, vertical angles are formed. If the angles are opposite to each other,they are sometimes referred to as vertically opposite angles. Vertical angles are used in real-lifesituations such as railroad crossing signs, letter "X", open scissors pliers, and so on. To ensurethat two intersecting lines were equal, the Egyptians would draw two intersecting lines and measure the vertical angles. Vertical angles are always equidistant from each other. In general, when two lines intersect,then two pairs of vertical angles are formed.Let’s Know More About Vertical Angles First and Then Jump toCongruent Angles● Vertical Angles TheoremThe vertical angles, defined as angles formed by two intersecting straight lines, are congruent.Vertical angles are always congruent with one another.● Is it True that all Vertical Angles are CongruentVertical (opposite) angles are always congruent, or equal to each other, no matter how we crossour pencils or how any two intersecting lines cross. In mathematics, it is known as the verticalangles theorem.● Congruent AnglesIf the corresponding sides and angles of two triangles are of equal size, they are said to becongruent. When two angles are superimposed, they are also congruent. It means if theycoincide with each other by turning and/or moving. A parallelogram's diagonals also createcongruent vertex angles.Applications of Vertical AnglesVertical angles are used in a variety of ways that we see or experience in our daily lives.● The roller coasters are set at a specific angle to ensure proper operation. These anglesare so critical that if they are shifted by a degree above or below, an accident couldoccur. A roller coaster's maximum vertical angle (Mumbo Jumbo, Flamingo Land) is 112degrees.● We see two vapour trails that cross each other and make vertical angles at an airshow.● Railroad crossing signs (X) are placed on roads to ensure the safety of vehicles. ● A kite is held aloft by two wooden sticks that form a cross.As we have already discussed what vertical angles are, let’s learn about the properties of congruent angles. Facts About Vertical Angles● Angles that are congruent - Vertical angles of equal measure are always congruent.● Vertical angle sum - Both pairs of vertical angles (for a total of four angles) always addup to 360 degrees.● Angles that are adjacent - Angles formed by each pair of vertical angles are referred toas adjacent angles, and they are supplementary (the angles sum up to 180 degrees).Four Congruence ConditionsThe triangle congruence criteria are as follows:● SSS (Side-Side-Side)Two triangles are said to be congruent if three sides of one triangle are congruent with threesides of another triangle.● SAS (Side-Angle-Side)Two triangles are said to be congruent if their two sides and included angle are congruent to thecorresponding parts of another triangle.● ASA (Angle-Side-Angle)The condition is as follows : Two triangles are known to be congruent if two angles and theincluded side of one triangle are congruent to the corresponding parts of another triangle.● AAS (Angle-Angle-Side)The condition is as follows: Two triangles are said to be congruent if their two angles and non-included side are congruent to the corresponding parts of another triangle.Congruent and Vertical angles is a vast topic, which can be easily learnt through cuemath - thebest Maths online tutoring platform.● HL (Hypotenuse-Leg, Right Triangle Only)So, the condition is if the hypotenuse and leg of one right triangle are congruent to thecorresponding parts of another right triangle, the right triangles are then said to be congruent. Tips and Tricks for Congruent Angles1. Equal angles are also known as congruent angles.2. Congruent angles are those that are vertically opposite one another.3. Congruent angles are all alternate angles and corresponding angles formed by the intersection of two parallel lines and a transversal.
Whitney M. Find a counterexample to show that the converse of each conditional is false. 1 Expert Answer
Phillip R. answered • 08/26/14 Top Notch Math and Science Tutoring from Brown Univ Grad
The converse is "If two angles are congruent, they are vertical angles" This is false. For example two angles of an isosceles triangle have the same measure (are congruent) but they are not vertical angles. |