PROOFS INVOLVING TRIANGLES

Given the following diagram, find the required measure. Given: m 3 = m 7 m 2 = 60° m 6 = 115° m 4 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page69b.gif

10

Given the following diagram, find the required measure. Given: m∠3 = m∠7 m∠2 = 60° m∠6 = 115° m∠1 =

120

Given the following diagram, find the required measure. Given: 𝘭 ∥ 𝘮 m∠1 = 140° m∠3 = 50° m∠4 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page70a.gif

130

Given the following diagram, find the required measure. Given: 𝘭 ∥ 𝘮 m∠1 = 140° m∠3 = 50° m∠2 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page70a.gif

40

Given the following diagram, find the required measure. Given: 𝘭 ∥ 𝘮 m∠1 = 140° m∠3 = 50° m∠5 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page70a.gif

40

If m∠1 = 3x, m∠3 = 2x + 20 and m∠5 = 30, what is the value of x? https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page69b.gif

50

Given the following diagram, find the required measure. Given: m∠3 = m∠7 m∠2 = 60° m∠6 = 115° m∠3 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page69b.gif

55

Given the following diagram, find the missing measures. m∠O = m P m∠1 = 36° m∠O= https://dw6y82u65ww8h.cloudfront.net/organisations/328/53db9646-e59f-4b8b-98ee-7ee949cd415f/page69a.gif

72

Given the following diagram, find the required measure. Given: 𝘭 ∥ 𝘮 m∠1 = 140° m∠3 = 50° m∠6 = https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page70a.gif

90

auxiliary line (Model 3)

A line introduced in a figure to make a proof possible.

corollary (Model 4)

A statement that is easily proved by applying a theorem.

exterior angle of a triangle (Model 1)

An angle formed by one side of a triangle and the extension of an adjacent side of the triangle.

remote interior angles (Model 2)

With respect to an exterior angle, the two interior angles of the triangle that are not adjacent to the exterior angle.

Given the following diagram, find the required measure. Given: m∠3 = m∠7 All of the following are true 𝘦𝘹𝘤𝘦𝘱𝘵 https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page69b.gif

m∠3 = m∠6 + m∠7

All of the following are equivalent except https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page70a.gif

m∠7 + m∠6

If the measure of angle 2 is twice the measure of angle O, then which of the following must be true? https://dw6y82u65ww8h.cloudfront.net/organisations/328/53db9646-e59f-4b8b-98ee-7ee949cd415f/page69a.gif

m∠P = m∠O

If one of the exterior angles of a triangle is acute, then the triangle must be

obtuse

Angles 4 and 5 form what type of angles? https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/page64a.gif

vertical angles

In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer. https://dw6y82u65ww8h.cloudfront.net/organisations/328/dee84033-da89-442d-8afc-8a6692bf3f1d/img_geou03l21_14.gif

• ∠1 and ∠4 are alternate interior angles. • m∠5 = m∠3 + m∠2. • m∠5 + m∠1 = 180.