The external angle is suplementary to the internal angle close to it. We also know that the sum of all the internal angles of the triangle are equal to 180 degrees, this means that the angle "a" is suplementary to the sum of the angles "b" and "c". Through this logic, we can conclude that since:
Then we can conclude that:
Therefore the statement is true, the exterior angle is equal to the sum of its remote interior angles.
Let's use an example:
On this example, the external angle is 120 degrees, therefore the sum of the remote interior angles must also be equal to that. Let's try:
The sum of the remote interior angles is equal to the external angle.
Hello :
<span>–9.5 + 6x ≥ 42.1
6x </span>≥ 42.1 + 9.5
6x ≥ 51.6
x ≥ 51.6/6
x ≥ 8.6
using interval notation: <span>[8.6 ; +∞[ </span>
Answer:
1. Opposite
2. angle-side-angle criterion
Step-by-step explanation:
Since ABCD is a parallelogram, the two pairs of <u>(opposite)</u> sides (AB¯ and CD¯, as well as AD¯ and BC¯) are congruent. Then, since ∠9 and ∠11 are vertical angles, it can be concluded that ∠9≅∠11. Since ABCD is a parallelogram, AB¯∥CD¯. Since ∠2 and ∠5 are alternate interior angles along these parallel lines, the Alternate Interior Angles Theorem allows that ∠2≅∠5. Since two angles of △AEB are congruent to two angles of △CED, the Third Angles Theorem supports that ∠8≅∠3. Therefore, using the <u>(angle-side-angle criterion)</u>, it can be stated that △AEB≅△CED. Then, applying the definition of congruent triangles, it can be stated that AE¯≅CE¯, which makes E the midpoint of AC¯. Use a similar argument to prove that △AED≅△CEB; then it can be concluded that E is also the midpoint of BD¯. Since the midpoint of both line segments is the same point, the segments bisect each other by definition. Match each number (1 and 2) with the word or phrase that correctly fills in the corresponding blank in the proof.
A parallelogram posses the following features:
1. The opposite sides are parallel.
2. The opposite sides are congruent.
3. It has supplementary consecutive angles.
4. The diagonals bisect each other.
Answer:
ASA
Step-by-step explanation:
SAS, it must go in order and SAS covers it up, Side, Angle, Side
Answer:
the last choice
Step-by-step explanation:
