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Two triangles that have two angles in common are congruent if the sides between the two angles are also congruent?
Yes you can. This is because a triangle can be solved by ASA (Angle Side Angle). To construct this first draw the side. Then put one angle on one end of the side and the other on the other end of the side. Then extend the lines on the angles until they intersect and the other sides and angle "just happen."
What else can I help you with?
The ray common to two adjacent congruent angles?
90 degrees
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
Can two right triangles that are not similar still have one congruent acute angle in common?
No, it’s false.
What do 2 dashes on a triangle mean?
Having two dashes on a triangle is common notation in arithmetic, specifically geometry. Two dashes mean that there is one dash each on two different lines of the triangle, and this indicates that the two lines are of equal length. This also means that the triangle is an isosceles triangle.
What are non adjacent angles that are congruent and share a common vertex?
Where two straight lines cross the "vertically opposite" angles are equal.
What shapes have congruent base angles?
Isosceles triangles have congruent base angles, meaning the angles opposite the equal sides are the same. Additionally, certain polygons, such as isosceles trapezoids, also have congruent base angles. In general, any shape with symmetrical properties may exhibit congruent angles, but isosceles triangles and isosceles trapezoids are the most common examples.
How do you Prove triangle ACD is congruent to triangle BDC?
Because Corresponding Parts of Congruent Triangles, there are five ways to prove that two triangles are congruent. Show that all sides are congruent. (SSS) Show that two sides and their common angle are congruent. (SAS) Show that two angles and their common side are congruent. (ASA) Show that two angles and one of the non common sides are congruent. (AAS) Show that the hypotenuse and one leg of a right triangle are congruent. (HL)
Two right triangles that are not similar still may have one congruent acute angle in common?
Not so. The two acute angles of a right triangle must add up to 90 degrees.So if the triangles have one congruent acute angle in common, they must alsohave the other acute angle in common, and then they're similar.
When can you say that 2 triangles are congruent?
Two triangles are congruent when they have the same shape and size, meaning all corresponding sides and angles are equal. The most common criteria for establishing congruence are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles. If any of these conditions are met, the triangles can be considered congruent.
What do all the angles in an intersecting line have in common?
That two of the Angles are Supplementary and two of the Angles are congruent.
What do congruent and similar figures have in common?
Their angles are the same.
True or false Two right triangles that are not similar still may have one congruent acute angle in common?
False. Assume that you had a two right triangles with one congruent acute (<90 degrees) angle in common. Let x represent the number of degrees in this angle in both triangles (which we can do since the angles are congruent). Let y represent the degree of the other angle in the first triangle and let z represent the degree of the other angle in the second triangle. We know that the sum of the degrees of the angles in a triangle is 180. So for the first triangle we have, 90+x+y = 180 For the second triangle, 90+x+z=180 Therefore, 90+x+y=90+x+z Subtract the 90+x from each side: y=z Therefore the degrees of the angles of the two triangles both are 90 [because they are both right triangles], x [because we said that this is the number of degrees of the congruent angles given in the problem], and y [because y=z]. Because the three angles of both triangles have the same measurement, the triangles must be similar.
What do equilateral triangles and acute triangles have in common?
All their angles are less than 90 degrees.
The ray common to two adjacent congruent angles?
90 degrees
Which pair of angles must be congruent?
An angle is the intersection of two rays with a common endpoint. Adjacent Angles are 2 angles that share a common vertex, a common side and no common interior points.
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
Can any triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
