Question

1. If AC measures 17 cm. What does AB measure?
A. 17 mm
B. 17 cm
C. 21 cm
D. 8 m
2. If ZA-90, what does 2D measure?
A. 75°
B. 80°
C. 90°
D. 109°
3. If AC measures 17 cm. What is the perimeter of the triangle above?
A. 51.04 cm B. 55.04 cm C. 58.04 cm D. 58.04 m
4. Since BC EF, given that EF is 24.04 cm. Then BC is
A. 24.04 cm B. 34.04 cm C. 90.04 cm D. 17.04 m
5. Since 2C = LF, given that B is 45°. Then ZE is
A. 45°
B. 95°
C. 180°
D. 270°​

Answer 1

Answer:

1. If AC measures 17 cm. What does AB measure?

solution B. 17 cm.

3. If AC measures 17 cm. What is the perimeter of the triangle above?

solution 17 +17 +24.04 = (c)58.04cm.

4. Since BC EF, given that EF is 24.04 cm. Then BC is

A. 24.04 cm

Answer 2

1. (Option B)

2. (Option C)

3. (Option C)

4. (Option A)

5. (Option A)

Given,

Two triangles ΔABC and ΔDEF

∠A$=90$°

∠B$=45$°

∠C=∠F

$AC=17cm\\BC=EF\\EF=24.04cm$.

To find,

1. Length of AB.

2. Measure of ∠D.

3. Perimeter of the triangle.

4. Length of BC.

5. Measure of ∠E.

Solution,

Let us start by finding ∠C in ΔABC,

We know that by angle sum property of a triangle,

$A+B+C=180$°

⇒$90+45+C=180$°

⇒$C=180-135$

⇒∠$C=45$°

And since

∠$C=$∠$B$

We can say that,

$AC=AB$

This is because sides opposite to equal angles in a triangle are equal.

Now in ΔABC and ΔDEF,

$AC=DF$

∠$C=$∠$F$

$BC=EF$

So, by Side- Angle- Side property of congruency of a triangle,

ΔABC ≅ ΔDEF

Hence,

$AB=DE$

∠$B=$∠$E$

Therefore,

1. $AB=17cm$ (Option B).

2.∠$D=90$° (Option C).

3. Since both the triangles are congruent, their perimeter will be equal.

⇒ Perimeter of triangle $=AB+BC+AC$

⇒$17cm+24.04cm+17cm$

⇒$P=58.04cm$ (Option C).

4. $BC=24.04cm$ (Option A).

5. ∠$E=45$° (Option A).