Help plz this is due today

Mathematics

2 answers:

Darya [45]3 years ago

6 0

Answer:

The three of them are similar.

Step-by-step explanation:

1- Triangle A and Triangle B have two same angles, 37° and 47°, which means the two angles are congruent. According to the Angle Angle Theorem (AA), in two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.

2- First, place both triangles correctly. When you do it, you'll notice that 24≅12, 32≅16, and 9≅4.5:

24/12 = 2 ✓
32/16 = 2 ✓
9/4.5 = 2 ✓

According to Side-Side-Side Theorem (SSS), if the measures of corresponding sides are known, then their proportionality can be calculated. If all three pairs are in proportion, then the triangles are similar.

3- Here, the triangle shows in each one two different angles, sharing only one which is 55°. To know if they are congruent, you can add the two different angles that show both triangles, 72° and 53°, with the 55°. If it gives 180, it means the can be congruent:

55°+72°+53 = 180° ✓

In-s [12.5K]3 years ago

5 0

Answer:

All three are similar!

Step-by-step explanation:

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$