{"id":232475,"date":"2025-06-12T01:24:26","date_gmt":"2025-06-12T01:24:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232475"},"modified":"2025-06-12T01:24:28","modified_gmt":"2025-06-12T01:24:28","slug":"if-each-quadrilateral-below-is-a-parallelogram-find-the-missing-measures","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/if-each-quadrilateral-below-is-a-parallelogram-find-the-missing-measures\/","title":{"rendered":"If each quadrilateral below is a parallelogram, find the missing measures."},"content":{"rendered":"\n

If each quadrilateral below is a parallelogram, find the missing measures. Date: Bell: Homework 2: Parallelograms This is a 2-page document! Directions: If each quadrilateral below is a parallelogram; find the missing measures MN = KN = ZK = iZL = MM = 15 31 CF = 7E = Cz = GD = 45 10 1198 N = D = 22 Given PQ = 24, PS = 19, \u00e2\u02c6 2 = 42, TQ = 10, \u00e2\u02c6 ZPQR = 106, \u00e2\u02c6 EQS = 498, and m\u00e2\u02c6 PRS = 35 QR = 8, PT = \u00e2\u02c6 ZQZS = \u00e2\u02c6 i2?QS = WL = PS = \u00e2\u02c6 ZPSQ = SQ = 4. Find KL 5. If AC = \u00e2\u02c6\u016114 and EC = 21 + 11, solve for : 7 – 2<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answers<\/strong><\/h3>\n\n\n\n

1. Parallelogram KLMN<\/strong><\/p>\n\n\n\n

    \n
  • MN =<\/strong>\u00a031<\/li>\n\n\n\n
  • KN =<\/strong>\u00a045<\/li>\n\n\n\n
  • m\u2220K =<\/strong>\u00a061\u00b0<\/li>\n\n\n\n
  • m\u2220L =<\/strong>\u00a0119\u00b0<\/li>\n\n\n\n
  • m\u2220M =<\/strong>\u00a061\u00b0<\/li>\n<\/ul>\n\n\n\n

    2. Parallelogram CDEF<\/strong><\/p>\n\n\n\n

      \n
    • CF =<\/strong>\u00a010<\/li>\n\n\n\n
    • FE =<\/strong>\u00a015<\/li>\n\n\n\n
    • CE =<\/strong>\u00a014<\/li>\n\n\n\n
    • GD =<\/strong>\u00a011<\/li>\n<\/ul>\n\n\n\n

      3. Parallelogram PQRS<\/strong><\/p>\n\n\n\n

        \n
      • QR =<\/strong>\u00a019<\/li>\n\n\n\n
      • SR =<\/strong>\u00a024<\/li>\n\n\n\n
      • PT =<\/strong>\u00a021<\/li>\n\n\n\n
      • SQ =<\/strong>\u00a020<\/li>\n\n\n\n
      • m\u2220QRS =<\/strong>\u00a074\u00b0<\/li>\n\n\n\n
      • m\u2220PQS =<\/strong>\u00a049\u00b0<\/li>\n\n\n\n
      • m\u2220RPS =<\/strong>\u00a039\u00b0<\/li>\n\n\n\n
      • m\u2220PSQ =<\/strong>\u00a057\u00b0<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Explanation<\/strong><\/h3>\n\n\n\n

        To solve these problems, we utilize the fundamental properties of a parallelogram. A parallelogram is a quadrilateral where opposite sides are parallel. This leads to several key geometric rules:<\/p>\n\n\n\n

          \n
        1. Opposite sides are congruent<\/strong>\u00a0(equal in length).<\/li>\n\n\n\n
        2. Opposite angles are congruent<\/strong>\u00a0(equal in measure).<\/li>\n\n\n\n
        3. Consecutive angles<\/strong>\u00a0(angles next to each other) are supplementary, adding up to 180\u00b0.<\/li>\n\n\n\n
        4. The diagonals bisect each other<\/strong>, meaning they intersect at their midpoints.<\/li>\n\n\n\n
        5. Alternate interior angles<\/strong>, formed by a transversal cutting across parallel sides, are congruent.<\/li>\n<\/ol>\n\n\n\n

          For Problem 1 (Parallelogram KLMN):<\/strong><\/p>\n\n\n\n

            \n
          • Side Lengths:<\/strong>\u00a0Opposite sides are congruent. Therefore, side MN is congruent to side KL, making\u00a0MN = 31<\/strong>. Side KN is congruent to side LM, making\u00a0KN = 45<\/strong>.<\/li>\n\n\n\n
          • Angles:<\/strong>\u00a0Opposite angles are congruent, so m\u2220L is congruent to the given m\u2220N, making\u00a0m\u2220L = 119\u00b0<\/strong>. Consecutive angles are supplementary. Thus, m\u2220K + m\u2220N = 180\u00b0, which means\u00a0m\u2220K = 180\u00b0 – 119\u00b0 = 61\u00b0<\/strong>. Finally, m\u2220M is opposite m\u2220K, so\u00a0m\u2220M = 61\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n

            For Problem 2 (Parallelogram CDEF):<\/strong><\/p>\n\n\n\n

              \n
            • Side Lengths:<\/strong>\u00a0Following the rule of congruent opposite sides, CF is congruent to DE, making\u00a0CF = 10<\/strong>, and FE is congruent to CD, making\u00a0FE = 15<\/strong>.<\/li>\n\n\n\n
            • Diagonals:<\/strong>\u00a0The diagonals bisect each other at point G. This means G is the midpoint for both CE and FD. Since FD = 22, GD is half of that, so\u00a0GD = 11<\/strong>. We are given that the segment CG = 7; because G is the midpoint, GE must also be 7. The full length of the diagonal is the sum of its parts:\u00a0CE = CG + GE = 7 + 7 = 14<\/strong>.<\/li>\n<\/ul>\n\n\n\n

              For Problem 3 (Parallelogram PQRS):<\/strong><\/p>\n\n\n\n

                \n
              • Side Lengths & Diagonals:<\/strong>\u00a0Opposite sides are congruent, so\u00a0QR = PS = 19<\/strong>\u00a0and\u00a0SR = PQ = 24<\/strong>. The diagonals bisect each other at T. Thus, PT is half the length of PR, making\u00a0PT = 42 \/ 2 = 21<\/strong>. Since TQ = 10, the full diagonal\u00a0SQ = 2 * TQ = 20<\/strong>.<\/li>\n\n\n\n
              • Angles:<\/strong>\n
                  \n
                • m\u2220QRS:<\/strong>\u00a0It is consecutive to \u2220PQR, so they are supplementary.\u00a0m\u2220QRS = 180\u00b0 – 106\u00b0 = 74\u00b0<\/strong>.<\/li>\n\n\n\n
                • m\u2220PQS:<\/strong>\u00a0Since PQ || SR, the transversal SQ creates congruent alternate interior angles. Therefore,\u00a0m\u2220PQS = m\u2220QSR = 49\u00b0<\/strong>.<\/li>\n\n\n\n
                • m\u2220PSQ:<\/strong>\u00a0Since PS || QR, m\u2220PSQ is the alternate interior angle to m\u2220RQS. We find m\u2220RQS by subtracting: m\u2220RQS = m\u2220PQR – m\u2220PQS = 106\u00b0 – 49\u00b0 = 57\u00b0. Thus,\u00a0m\u2220PSQ = 57\u00b0<\/strong>.<\/li>\n\n\n\n
                • m\u2220RPS:<\/strong>\u00a0Since PS || QR, m\u2220RPS is the alternate interior angle to m\u2220PRQ. We find m\u2220PRQ by subtracting: m\u2220PRQ = m\u2220QRS – m\u2220PRS = 74\u00b0 – 35\u00b0 = 39\u00b0. Thus,\u00a0m\u2220RPS = 39\u00b0<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                  \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                  If each quadrilateral below is a parallelogram, find the missing measures. Date: Bell: Homework 2: Parallelograms This is a 2-page document! Directions: If each quadrilateral below is a parallelogram; find the missing measures MN = KN = ZK = iZL = MM = 15 31 CF = 7E = Cz = GD = 45 10 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-232475","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232475","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=232475"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232475\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}