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:
D. AC ≅ XZ
Step-by-step explanation:
To prove that two triangles are congruent by the Angle-Side-Angle theorem, both triangles must have two corresponding angles that are congruent to each other in each triangle, and also a corresponding included side in each triangle that are congruent.
Thus, we are given that,
<X ≅ <A and <Z ≅ <C, therefore, what is needed is a corresponding included angle in each triangle that are congruent to each other, which are,
AC and XZ
Therefore, what is needed is:
AC ≅ XZ
Answer:
1st, 3rd, and 4th box.
Step-by-step explanation:
9^5=59049
9^2=81 9^3=729 729*81=59049 yes
9^5=59049 59049x9=531441 no
9^4=6561 6561*9=59049 yes
9^2=81 81x81=6561 6561*9=59049 yes
9^3=729 729x729=531441 no
