Deductive Geometry II

Which proof shows that ∆ADO ≅ ∆ABO

• SSS

• SAS

• ASA

• RHS

Answer explanation

Both triangles share the side AO.

∠AOB = ∠AOD (Supplementary -- adding to 180°)

AB = AD (given) - this is the hypotenuse.

Thus, they are congruent through RHS.

What proof shows that ∆AEB≅∆DEC?

• SSS

• SAS

• ASA

• RHS

What proof shows that ∆WXY≅∆YZW?

• SSS

• SAS

• ASA

• RHS

Answer explanation

∠ZWY = ∠XYW (Alternate angles)

∠XWY =∠ZYW (Alternate angles)

WY is shared between both triangles.

Thus, both triangles are congruent by ASA.

What proof shows that ∆PTS ≅ ∆QTR?

• SSS

• SAS

• ASA

• RHS

Answer explanation

∠SPR = ∠QRP (Alternate Angle Theorem)

∠PSQ = ∠SQR (Alternate Angle Theorem)

PS = QR (given)

Therefore, the triangles are congruent by ASA.

What is the scale factor between these similar triangles?

• 1.5

• 0.67

• 7.5

• 1.1

Answer explanation

Dividing 2 by 3 is 0.67 roughly.

Dividing 3 by 2 is 1.5.

The scale factors can thus be 1.5 or 0.67.

What proof shows that these triangles are similar?

• AAA

• SSS

• SAS

• RHS

Answer explanation

∠ACB = ∠ECD (shared)

∠CED = ∠CAB (Corresponding angles)

∠CDE = ∠CBA (Corresponding angles)

Thus the triangles are similar by AAA.

What are the values of g and f?

• g = 8

  f = 9

• g = 8

  f = 6

• g = 6

  f = 8

• g = 9

  f = 8

Answer explanation

∆ADE ∼ ∆ABC (AAA by shared angle and corresponding angles)

AB value of 2 is scaled by 3 to become AD value of 6 = 4 + 2

Thus AC value of 4 -> 4 x 3 = 12 -> AE is 12 and g is 8.

BC value of 3 -> 3 x 3 = 9 -> f = 9.

Find the value of the pro-numeral in the diagram at right.

• 2

• 1

• 4

• 8

Answer explanation

Scale factor is actually 2 not 1.

PB is scaled to PR, with 4 scaled to 8 (4 + 4).

Find the values of x and y.

• Impossible to determine

• x = 4

  y = 3

• x = 0.75

  y = 16

• x = 3

  y = 4

Answer explanation

PQ value of 3 is scaled by 2 to become ST value of 6.

y = 8 / 2 = 4

x = 1.5 x 2 = 3