What Is The Measure Of Angle J In The Triangle Below Drawing Is Not To Scale

Triangle given two angles and the included side (ASA)

This page shows how to construct a triangle given one side and the bending at each end of information technology with compass and straightedge or ruler. It works by starting time copying the line segment to form 1 side of the triangle, then copy the ii angles on to each cease of it to complete the triangle. As noted below, at that place are 4 possible triangles that exist fatigued - they are all correct.

Multiple triangles possible

Information technology is possible to draw more one triangle has the side length and angle measures as given. Depending on which end of the line y'all draw the angles, and whether they are to a higher place or below the line, four triangles are possible. All four are right in that they satisfy the requirements, and are congruent to each other.

Note: this is not always possible

Geometry construction with compass and straightedge or ruler or ruler

It is not always possible to construct a triangle from a given side length and 2 angles. See effigy on the correct. If the two given angles add to more than 180°, the sides of the triangle will diverge and never run into. See Interior Angles of a Triangle.

Printable step-by-step instructions

The above animation is bachelor equally a printable footstep-by-step instruction canvass, which can be used for making handouts or when a computer is not available.

Proof

The image below is the final cartoon in a higher place with the ruby-red items added.

	Argument	Reason
1	Line segment JL is congruent to AB.	Drawn with the same compass width. For proof see Copying a line segment
2	The angle KJL is coinciding to the angle A	Copied using the procedure shown in Copying an angle. Encounter that page for the proof.
3	The angle KLJ is congruent to the angle B	Copied using the procedure shown in Copying an angle. Encounter that page for the proof.
4	Triangle JKL satisfies the side length and two angle measure given.

- Q.Eastward.D

Try information technology yourself

Click here for a printable worksheet containing ii ASA triangle construction issues. When you become to the page, use the browser print command to print every bit many equally you wish. The printed output is non copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of north line segments
Difference of 2 line segments
Perpendicular bisector of a line segment
Perpendicular at a point on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Dissever a segment into due north equal parts
Parallel line through a indicate (angle copy)
Parallel line through a point (rhombus)
Parallel line through a bespeak (translation)

Angles

Bisecting an angle
Re-create an bending
Construct a 30° angle
Construct a 45° angle
Construct a 60° angle
Construct a 90° bending (right angle)
Sum of northward angles
Difference of two angles
Supplementary bending
Complementary angle
Constructing 75° 105° 120° 135° 150° angles and more

Triangles

Copy a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and altitude
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given i side and side by side angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given two sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (outside case)

Right triangles

Correct Triangle, given one leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Correct Triangle, given hypotenuse and 1 angle (HA)
Right Triangle, given one leg and one angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the heart of a circumvolve
Circumvolve given 3 points
Tangent at a point on the circumvolve
Tangents through an external point
Tangents to ii circles (external)
Tangents to two circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Square given 1 side
Square inscribed in a circle
Hexagon given 1 side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circumvolve

Non-Euclidean constructions

Construct an ellipse with string and pins
Notice the center of a circle with any right-angled object

Source: https://www.mathopenref.com/consttriangleasa.html

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