MATH SOLVE

4 months ago

Q:
# Match the statements with their values

Accepted Solution

A:

Tile 1:

In any triangle (regardless its type), the sum of measures of the internal angles is 180°.

This means that:

∠ABC + ∠BAC + ∠ACB = 180°

Tile 2:

The sum of measures of internal angles of a triangle is 180°.

We are given that:

ΔABC is isosceles where AB = AC

This means that:

∠ABC = ∠ACB

We are also given that measure angle BAC is 70 degrees

180 = ∠ABC + ∠ACB + 70

∠ABC + ∠ACB = 110°

We know that both angles are equal, therefore:

∠ABC = ∠ACB = 110/2 = 55°

Tile 3:

We are given that ΔQPR is an isosceles triangle where PQ = QR

This means that:∠QPR = ∠QRP

We are given that ∠QRP = 30°

This means that:∠QPR = 30°

Tile 4:

A diagram representing the given scenario is attached.

Now we have:

point D is midpoint to AB and point E is midpoint to BC

There is a theorem stating that: "In a triangle, a line joining the midpoints of two sides is parallel to the third side and equals half its length"

Applying this to the givens, we would conclude that:ED is parallel to AC

Now, since these two lines are parallel, then angles BAC and BDE are corresponding angles which means that they are equal.

This means that:∠BAC = ∠BDE = 45°

Hope this helps :)

In any triangle (regardless its type), the sum of measures of the internal angles is 180°.

This means that:

∠ABC + ∠BAC + ∠ACB = 180°

Tile 2:

The sum of measures of internal angles of a triangle is 180°.

We are given that:

ΔABC is isosceles where AB = AC

This means that:

∠ABC = ∠ACB

We are also given that measure angle BAC is 70 degrees

180 = ∠ABC + ∠ACB + 70

∠ABC + ∠ACB = 110°

We know that both angles are equal, therefore:

∠ABC = ∠ACB = 110/2 = 55°

Tile 3:

We are given that ΔQPR is an isosceles triangle where PQ = QR

This means that:∠QPR = ∠QRP

We are given that ∠QRP = 30°

This means that:∠QPR = 30°

Tile 4:

A diagram representing the given scenario is attached.

Now we have:

point D is midpoint to AB and point E is midpoint to BC

There is a theorem stating that: "In a triangle, a line joining the midpoints of two sides is parallel to the third side and equals half its length"

Applying this to the givens, we would conclude that:ED is parallel to AC

Now, since these two lines are parallel, then angles BAC and BDE are corresponding angles which means that they are equal.

This means that:∠BAC = ∠BDE = 45°

Hope this helps :)